I live up in Miyako, Iwate, moved here about two months ago. I'd be more than happy to have you up for a weekend, but it's a little far from Tokyo - about 2 hours on the Shinkansen to Morioka and another 2 on the local bus.
I was just down this weekend with some friends - had a blast. Here's a few snippets:
Shinjuku - Most 'stereotypical' Tokyo neighbourhood with lights, clubs, shops, restaurants abound - a little seedy at times, but overall a good place to spend a few nights.
Shibuya - Home to the busiest pedestrian crossing in the world. Always filled with people, my favourite place to go out at night. Look out for the love hotels; they're quite a fun experience if you have the opportunity
Harajuku - Not much here other than the famous Cosplay girls who hang out on the nearby bridge to the JR Yamanote line station. Stop in on your way to/from Shinjuku/Shibuya but don't plan on spending more than an hour or so
Ginza - Shopping district. If you want to buy clothing, shoes, watches, jewelry, or to window shop; go here. They also have tons of good restaurants (albeit pricy)
Asakusa - "Old Tokyo" the Shoji temple is the main attraction here, a worthwhile trip. Also, the "flamme d'or" and multiple capsule hotels can be found here.
Tsukiji - The famous fish market. If you want the freshest sushi; this is your destination.
Yokohama - A suburb of Tokyo but the 2nd largest city in Japan. You'll find the tallest building in Japan here as well as the largest Chinatown. I really enjoyed my time in Yokohama and highly recommend the 1 hour trip out. Heh, be sure to stop in at the Anpanman children's museum - hilarious.
Chiba - Home to Tokyo Disney and Sea Disney. Long lines on the weekend so be sure to go during a day off. It was a lot of fun with my friends.
Ueno - Museums and the Tokyo Zoo. The zoo was one of the best bargains, many animals specific to Asia that I'd never seen before.
Akihabara - The electronics district. Have to go to Yodobashi Camera if you are remotely interested in consumer electronics or computers, incredible place. The neighbourhood has hundreds of smaller shops as well selling every possible type of electronic gadget and specialty shops (host/hostess clusb, maid cafes, and any type of unique clothing/costumes).
I won't comment on Roppongi or any other place as I haven't had any first-hand experiences there.
Not knowing Japanese won't be a problem if you keep to the touristy areas. I'd suggest picking-up a travel phrasebook though so you aren't totally lost in conversations if need be.
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