What to do for a month?

I will be in Arakawa/Taito area for a month this summer and I need some things to do. I'm not big on schedules, so I pretty much just wanted to do stuff as I went along. But I just need ideas of what there is to do. I'm 18, so I was thinking about Shibuya/Shinjuku/Harajuku. And I like cars, so maybe Daikoku Futo (If I can get my friend in Yokosuka to drive me home afterwards)
I've already decided I'm going to Tokyo Dome City, Nippon Budokan, and I'm going to try for an onsen or a ryokan for 1 night. I'd also like to see rainbow bridge at night.

But contrary to the typical teen, I also like sightseeing things. But I do also want to visit amusement parks (not sure how big Tokyo Dome is)

I'm sure I'm leaving some things out, but suggestions would be great. My intentions are to finish college and go there to teach English on a workers visa. (or something else seeing as I'll be taking Japanese language course in college) So I want to make this a trip to remember.

Thanks in advance

Is there any reason why you want to stay there for 1 month? You can cover a LOT of places in Japan for 1 month if this is a leisure trip/vacation. Taito and surrounding don't have enough to last you 1 month

Seeing rainbow bridge at night is best to be done over at Daiba.

For the night of Onsen, I'd recommend changing it to 2 nights and go over to Kinugawa for this, you can visit nikko and drive up/down irohazaka too

I just randomly chose to stay a month. But yeah, this is just a leisure trip, no priorities.

How much would 2 nights at an onsen be? If I were to do that, I'd probably want to do it with friends.

I'm not sure if I would want to go that far out for an onsen. This is my first time in Japan, so I'm not too familiar with how everything is layed out. I'd prefer to stay in/near Tokyo.

Are there any other theme/amusement parks in/near Tokyo other than Dome city and Disney?

As long as you do a tiny bit of research, it's very easy to get between cities in Japan (in fact, you'll probably find travelling between cities much easier than trying to navigate Tokyo streets!)

It depends on where you go and the type of onsen. Some hakone resort pose themselves as "REAL" onsen, when they really just have a giant water heater running. Onsen, real ones and good ones usually cost around 150 a night for double occupancy, no meal plan.

The best onsen resort I've been to is Yume no Toki in Kinugawa, i believe it was about 280 USD double occupancy with a meal plan.

There is NOTHING in Tokyo area/region that will last you a month. If you really like Tokyo, I will suggest that you spend 10 days out of the month to visit Kyushu, Osaka (Include Kobe, Kyoto, Nara etc). Spend 2 days in Yokohama. And the rest of the trip you take it easy around Tokyo.....