Even if you're just staying in Tokyo you will still have more than enough to do in or around the main city, especially since you're staying in Shinjuku. If you want the onsen experience without having to travel several hours outside of the city and paying a lot as well, just check out one of the touristy "mega onsen" type establishments downtown, the two biggest ones being Odaiba Onsen Monogatari across the water from Shinagawa, or there's also Spa Laqua in Suidobashi next to the Tokyo Dome. Both will run in the 2,500 yen/person range for an all day pass and are essentially massive complexes with various types of baths, as well as other options for amusement such as food courts, massage (legit) services, relaxation rooms and, most importantly, alcohol.
Of the two, I'd say Odaiba has bigger and better bath options but shittier food and is more geared towards tourists and families. You dress up in a Japanese robe while in the common areas where there are also all sorts of games for kids to play. Again, I only go because of the better rotenburo and proximity to Gotanda, where I often go afterwards for fantastic craft beers and an enthusiastic akasuri and HE with a naked middle-aged Korean lady. Spa Laqua is definitely geared more for adults, is quieter, has a fantastic lounge area to relax in a recliner, and the bathing area is smaller but a little more refined. It's also a bit more expensive all around, with better restaurants and upscale body care services (legit).
But as far as summers go, the only thing I really like about summer is beer gardens and there's one I'm definitely planning to try next. I don't know what sort of day adventures you're after but when I'm in town next month I'm planning to hit this attraction they call "Beer Mount," up on Mt. Takao, which is about an hour outside the city. You can either hike or catch a cable car all the way up Takaosan, where there's a massive beer garden complex which runs about $30usd/person for a couple hours of all you can eat and drink.
Do a Google search on it, looks pretty fun. You and your squeeze can take the ski lift chairs all the way up, get shitfaced at the top of a mountain then slip off into the deserted descending forest trails and get your Brokeback Mountain on. And when you finally get to the bottom, there's supposedly a nice little onsen you can stop at to wash all the sweat and forest debris out of your asscracks. Maybe I'll see you there??
Awesome. Just looked it up and looks like a done deal. Food and alcohol? And all you can eat? You just strummed the heartstrings of this American .