In regards to character restaurants, there are a few restaurants in each park that have character dining.
DisneySea: Horizon Bay, Cape Cod Cook-off
Disneyland: Crystal Palace, Polynesian Terrace, Diamond Horseshoe
I have been to Horizon Bay, Cape Cod Cook-off, Crystal Palace, and Polynesian Terrace. Horizon Bay is more geared towards character greeting, centered on Mickey and Friends in special costumes that can only be seen at the restaurant. I don't recall seeing any face characters. Polynesian Terrace is, as the name suggests, Hawaiian themed and has a luau show and characters appear on stage. There are character greetings but it isn't as much compared to Horizon Bay.
Crystal Palace is a buffet and, while it says it has character greeting, I have never actually seen characters in the handful of times I have been there. I hear that Pooh and friends occasionally come out but it is very rare. As for Diamond Horseshoe, it is Western-themed so think saloon-style atmosphere and cowboys including a special scene on Woody's Round-Up from Toy Story.
Here's the thing - with the exception of Crystal Palace and Cape Cod Cook-off, character dining restaurants require reservations. It is not a walk-in restaurant. Online reservations are available but they are only in Japanese. There is an English-service number you can call to make reservations though and you can find it here
https://reserve.tokyodisneyresort.jp/en/far/inquiry_01 or here
http://www.tokyodisneyresort.jp/en/info/
If you already know the dates you are going, I highly suggest that you make a reservation ASAP. Reservations open a month in advance and they go REALLY fast, as in fully booked in two days, especially in regards to the Polynesian Terrace.