As for a place to stay, I recommend gaijin houses, they are way cheaper than hotels. The biggest problem with them is, that you need to stay there longer as well. But they should be about 100 000 yen for a month inside Tokyo, or if you can sleep in the same room, you usually have to pay some extra, but it is still cheaper than renting two rooms instead.
Money wise, that should be more than enough. The daily use of money should be somewhere around 1000 to 2000 yen, or more depending how expensive you want to eat. The gaijin houses also have a kitchen that you can use, so you could save money by cooking yourself.
I myself, recommend you to stay away from McDonalds and other non-Japanese fast food chains, as they are rather expensive in Japan. A bowl of ramen usually costs around 500 to 1000 yen and is very taste and the bowl is usually big.