If you stick to the big cities and tourist sites in Japan you should be fine even if you don't speak a word of Japanese. It's a different story if you're out in the countryside...but that's true in most countries. English is an international language (ignoring native speakers for a second, no language comes close in terms of how many people learn it as a second language) and any place that deals heavily with tourists (like hotels, etc.) will have somebody on staff who can speak it. I think where you'll have the most trouble is in restaurants. Sure some places have English menus, but then you're limiting yourself to the more touristy places (which aren't necessarily the best...). It can be hard to get a truly authentic food experience without knowing the language or having some sort of guide.
Also, navigating Japanese maps can be a pain in the ass even if you know some Japanese because location names are all in kanji and proper names have their own set of rules. Even native speakers won't necessarily know how to pronounce the name of every city, street, etc. if they haven't been there before. Seriously, Japan, but some furigana on your maps...you might think to just buy a tourist map that's in English (or use your GPS or whatever it is the kids do these days...), but the thing is you can't actually compare that to the signs you see since those signs are in kanji. You need something with both.
In terms of cost...well, given how much a flight to Japan costs I would recommend spending around two weeks there (or more if you can swing it...) to make it worth it. Seriously, those flights aren't cheap. You can stay for surprisingly little in Japan, though. I know a lot of people say it's an expensive country (an it is in some ways), but I was able to find rather cheap hotels that were still quite nice. I stayed in major cities for under $40 a night. Honestly, I'm not sure Japan even has dive hotels the way we do in the US. As you go down in price the rooms get smaller (they can get very small indeed...), but they always seem clean and safe. And what do you really need besides a bed? I assume you're going to be out and about most of the day, not sitting around in a hotel room. Like most places, food prices vary a lot depending on what you're getting. Good but cheap options are things like ramen, okonomiyaki (seriously, if you've never had it you have to try it), and donburi.
Finally, don't limit yourself to Tokyo. Well, Tokyo is huge...feels more like several different cities connected together. But even so there are so many places to see in Japan. The shinkansen (bullet train) is a great way to get around, and there are rail passes available for tourists that give you unlimited rides. They're kind of pricey, though, so I do recommend doing the math to see if it's actually worth it. They make sense if you're going to be traveling between cities a lot but not necessarily if you're only going a couple places.