Probably flying out of Dulles, east coast US. Ideally I'd like to see a few different cities. But yeah, I'd be okay with cheaper accommodations; as long as it's a place to sleep where I can keep my stuff, I'm not picky. A hostel or capsule hotel would be fine.
Ok. When I fly back to Florida from Hiroshima I stop in Tokyo and then Dulles. Since you'll most likely be going from Dulles to Narita in a straight shot, your tix will probably be a bit cheaper than mine. From Hiroshima to Florida round-trip in December I've been paying an average of $1600. This is with ANA, which is a pretty awesome airline. If you're lucky, you might be able to snag tickets for just over a grand, but I doubt you'll be able to find much cheaper.
You'll also need to find out if you need a JR pass or not. If you want to hit up major cities like Tokyo, Osaka, Kyoto, Hiroshima, etc., then you'll probably need one. If you're just doing Tokyo and the outskirts you probably won't need one. A two-week JR Pass goes for roughly $600.
Are you a foodie? Tokyo is a gourmet city with a treasure trove of amazing places to choose from. I'm not saying you need to be dropping fifty bucks for every meal, but if you only budget enough for 400 yen gyudon for every meal then I feel like you'd really be missing out.
For accommodation, it looks like the average price of a capsule hotel is between 20-40 a night. I've stayed at cheap places in Tokyo like Sakura House before and I think that was like 40-50 per night.
Yeah, so no matter how you slice it I don't think 2 grand is going to be enough. Maaaaybe 3 grand depending on how much your plane ticket costs, but I think I would recommend closer to 4.