Avoid the Rush
If you want to eat at TDR, you may face some challenges. The restaurants, like everything else, are incredibly busy, and waiting an hour or more in line to get in to a restaurant (Grandma Sara's Kitchen and Horizon Bay spring to mind), is not uncommon!
There are ways around this of course though. If your hotel offers breakfast, eat it. And fill up! That way you can hold over until the main lunch time rush has passed and actually find somewhere to sit.
Things to Consider
Food is generally very good, but comes in very small portions, and can cost a fortune. The drinks cups across the parks are tiny even by European standards, but water fountains with small cups are provided for free in nearly all restaurants, so you can take as much as you want of that.
You'll also come to discover that beverages are inconsistent throughout the resort, even at the major restaurants. In some places you'll find certain drinks, and others they will be different. Coca-Cola is not standard across the board, especially if you want Diet Coke/Coke Zero! If you're a Sprite lover like me, you'll also find you might have to try other drinks!
Food is expensive, and portions small
Sadly, many of the table service restaurants and buffets in the parks are by reservation only, and can only be reserved in advance, online, in Japanese. Luckily we have a Japanese friend who can do this for us, but otherwise it is very difficult. Sometimes, if you're lucky, there might be space if you enquire directly at the restaurant (we've done this, and it can work), but more often than not, you'll be turned away.
Dining in Tokyo Disneyland
We found that the Plaza Restaurant (which faces into Central Plaza but is technically part of Tomorrowland), is often quiet during the afternoons. Similarly, Tomorrowland Terrace in Tomorrowland offers a large seating area, and can be less busy outside main meal times. It's a good place for burgers and fries.
Food at Lucky Nugget is pretty good
We discovered that the Hungry Bear Restaurant in Westernland was nothing like its Disneyland CA counterpart, and offered some really decent curry meals. I don't eat anything spicy, and was absolutely fine with what they offer.
Also in Westernland, the Lucky Nugget Cafe offers some fairly decent "western" food, with pretty riverside seating, next to the Rivers of America. It's a bit secluded, so it doesn't get as busy as other places in the park. You can also find churros here.
We also really liked the food at Queen of Hearts Banquet Hall, but that is always mega busy, and probably not worth the hour wait just to get in. The Sweetheart Cafe in World Bazaar has some good sandwiches and pastries, for those wanting lighter options.
If you're able to get reservations (which is likely to be nearly impossible), I also would recommend the Lilo and Stitch lunch show at the Polynesian Terrace in Adventureland. The food was great, and the show is cute. Plus, the characters come down and meet guests too, unlike any other dinner show I've ever been to.
On the subject of dinner shows, there are three others inside TDL that are worth mentioning. At the Polynesian Terrace you can enjoy dinner with Mickey and Minnie at the Polynesian Paradise show. The Diamond Horseshoe in Westernland has two shows also. At lunch you can join the Toy Story gang in the Horseshoe Roundup, and at dinner Mickey and Company is especially great.
Popcorn is a BIG thing in Tokyo, and you can find a LOT of really cool, and often disgusting, flavours!
Popcorn buckets are like the Holy Grail, and the Japanese go nuts for popcorn and the buckets. Flavours and bucket designs can vary by location, season and event (for example you may find a Winnie the Pooh one near Pooh's Hunny Hunt, or a Halloween one in Westernland during October).
Expect to wait in long lines for popcorn at any time of the day, pretty much anywhere across the parks.
Dining in Tokyo DisneySea
The food at Zambini Brothers is decent
In Tokyo DisneySea, I really like Zambini Brothers, which is an Italian counter service place in Med Harbor. Lines can be long, but manageable, here.
We also quite like Casbah Food Court (counter service) in Arabian Coast, which also serves curry. Again, I like it, and don't normally like curry!
Sebastian's Calypso Kitchen in Mermaid Lagoon offers some good burgers, fries, and desserts.
Our dining experiences at TDS are a bit more limited than TDL, for a number of reasons. The main one is that, honestly, the crowds and lines to get into most places is beyond what I call acceptable, and we would either go back to TDL, or to some place in Ikspiari, such as the Rainforest Cafe.
Also, dining options, at least I felt, were more limiting in TDS than TDL, with less good counter service, and more exorbitantly priced table service.
Dining at Ikspiari and the Hotels
If you want to escape the parks for a while, and want to find a decent sized "Western" meal, then go to the Rainforest Cafe in Ikspiari. The food and drinks are similar to the US and Europe, and I think they offered refills too, from what I recall. Obviously RFC isn't the height of cuisine, but when you've had a really hectic day in the park, with little to eat and drink, you'll appreciate the American sized burger and fries, trust me! I will add though, that some of the options definitely do have a Japanese "twist", and while it's certainly a safe house for Westerners, just beware that some dishes might come prepared a little different to what you expect!
Ikspiari also has a TGI Friday's and a Starbucks for those seeking other Western fare.
We have had dinner at Oceano at the MiraCosta, which overlooks Med Harbor. It's a really good buffet, with great park views, but very expensive.
If you time your reservation right, you can get terrace/balcony priority viewing of any of the water shows in Med Harbor, for no extra cost. When the show is about to start, the doors will open and you can leave your table, and head onto the terrace to view the show.
Chef Mickey at the Ambassador
The other hotel restaurant we dined at - that is worth recommending - is Chef Mickey at the Ambassador.
It's another buffet, and is a character meal (what did you expect with the name Chef Mickey?).
You'll usually find four of the Mickey and friends characters in attendance, wearing specially themed costumes.
The Japanese parks are filled with a wide range of wonderful, and often wacky, snacks and treats. They always seem to change what is on offer, too, which keeps things interesting! Some of the more interesting things we have tried include sundaes with a multitude of toppings, brownies, cakes and sweet dumplings with varying fillings to multiple flavoured churros, seasonal desserts in souvenir cups and tipo torta, and much more!
Bars and Lounges
While I admit our experience of bars and lounges at TDR is limited, I thought it worth mentioning that we have had drinks at both Magellan's Lounge and the Teddy Roosevelt Lounge at TDS. Both offer classy, air conditioned, quiet settings away from the hustle and bustle of the parks. The Teddy Roosevelt Lounge especially made me feel like I was drinking in an exclusive bar on a high end cruise liner!
Vegetarian and Vegan Dining
Since I initially prepared this planner, Jon and I have become vegetarian. I can honestly say that vegetarian dining in Tokyo Disney Resort is a definite challenge, and sadly vegan dining is near impossible. There are just four restaurants that officially offer one vegetarian meal option each. At Tokyo Disneyland the two options are Eastside Cafe in World Bazaar and Hungry Bear in Westernland. In Tokyo DisneySea there is Restaurante di Caneletto and Zambini Brothers, both in Med Harbor.
Let's start with the table service options (Eastside and Caneletto). We have tried both, and honestly they were really good. The food portion sizes for both dishes were actually decent, which is a relief for Tokyo dining, and had a lot of flavour. The downside of course is that both locations are table service and can be quite pricey - not to mention you need reservations to eat at them. Thankfully, even though reservations are recommended, we haven't ever encountered a problem with a walk-up request, although, I can't guarantee that'll always be the case.
The counter service options - Zambini and Hungry Bear - were also both very good. Zambini has just one margherita pizza, and Hungry Bear has a vegetable curry dish. The vegetable curry is actually one of our favourite things to eat at TDR.
Of course, many snacks and treats across the parks are usually meat free too - though be careful with sundaes and the like, as they nearly always have jelly (jello) in them, which of course contains gelatine.
We have also found many restaurants (though not all) to be quite accommodating if you ask to speak to a manager. The Pan Galactic Pizza Port in TDL was able to prepare for us a meat free pizza, even though there was literally nothing on their menu that was vegetarian friendly!
The final option would be to dine at buffets, and while these are expensive (and of course usually require reservations), it gives you the flexibility to choose. Chef Mickey at the Ambassador Hotel was one of the highlights of our trip last time because the chef was specially able to prepare for us a huge pasta dish and a pizza - each! - as well as having all the meat-free options on the buffet! They were super friendly and very accommodating.
One final tip. Vegetarian in Tokyo can literally mean you "prefer" vegetables, as opposed to not eating meat at all. Even if the Japanese say something is "vegetarian", it could well just have more vegetables in it! We have found that if you use the internet to translate "I do not eat meat or fish" (using Google Translate or the like), and literally have a print out or a screenshot of that to show the person serving you, they will understand what you mean and try to find a solution to the "everything here has meat in it" problem.