Depends what you are into, but for some, the best, and only place to go out, is Roppongi. For a quieter time in comparison, try Shinjuku.
Are you there on business, and if so what part of Tokyo? It is unbelieveably massive. For an experience try a Capsule hotel. Or, if the opportunities, how about a place like this? For a decent but no-frills place, look at something like the Toyoko Inn, with rooms at about 40-60 euros a night. There are loads of them. You're better off with a hotel near wherever you will be working, but if you want to stay near where you're going out, the Yamanote line will get you pretty much wherever you need to be.
Shinjuku has the Metropolitan buildings that have an observatory which is amazing at night. Can't remember if you have to pay or not. Interested in baseball? Check out the Yomiuri Giants at home, or head to the Imperial Palace, although you don't really get near it.
This website should have some decent info for you on all aspects of travel, including good hotels. Their forum is pretty helpful also.
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