If you're looking for a quiet 2-day 1-night get away you could head to Hakone. It's about 1 hr outside of Tokyo and boasts some very nice onsens. It's just 1 express train from Shinjuku, about 1500yen. You can get the Hakone pass through Odakyu Railyway Co. which entitles you to a return train ride and access to the sites while you're there, i think the total thing is 4500yen. That doesn't include accomodations.
If you're looking for interesting independent clothing shops, restaurants and little hide-away bars Shimokitazawa is a cool spot, you can stop off there on your way back from Hakone. It's on the same line as the train to Hakone. For more shopping, take the Keio from Shimokitazawa to Kichijoji. In Kichijoji there is also a small zoo and a park, tons of shops.
If you'd like to take a daytrip and see the ocean, I highly recommend Katase Enoshima. It's easily accessible from the Odakyu line, make your way to Sagami-Ono and change there, the line branches off towards Hakone Yumoto and Katase Enoshima. In Enoshima, you cross a large bridge, hike over a hill (which has many interesting little noodle houses) and end up on the other side looking at the ocean. (see pic below). In Enoshima there is also a very nice aquarium. Good for a day trip.
I never ventured too far from Tokyo but I made it to Kobe, Osaka and Kyoto. In Kobe I highly urge you to check out the earthquake memorial museum. It's a short bus ride from Kobe's main station Sannomiya and will give you an appreciation for how far the city has come since the earthquake of 1995 devastated it. Osaka and Kobe are only 20mins apart by train so its easy to do and very educational. While in Kobe I also recommend the portside area, there are some nice cheap boat cruises around the port available. Those two things together are good for a day in Kobe.
Osaka.. there's Universal Studios, the Namba area, and it also has a very nice aquarium at Osakako station on the Chuo subway line. Universal studios is good for a day, and the aquarium during the daytime and Namba at night also make for a good day, everythings very close-by and accessible in Osaka.
That's all I can think of for now, in Kyoto I stayed with my cousin and did not have to plan anything myself, all I can tell you is that there are many nice shrines and temples there obviously so its definitely worth going to. The Higashiyama (east mountain) area is especially nice, lots of little souvenier shops and a very famous shrine whose name I can't recall right now.
Here are some photos, individual results may vary!
Enoshima:
Hakone:
Kobe portside area: