Hello,
I'd like to know what kind of nightlife you're interested in order to give you a bit more info.
There are islands very near the city, like Spetses and Hydra, which do have nightlife, bars, and good food (not the BEST beaches, but very nice they are).
Mykonos is the only island in Greece with cosmopolitan sort of nightlife (big clubs with international djs).
The others have pretty good nightlife, but not as 'wild'.
Paros is a very good option, as mentioned by some of the others in this thread.
Andros is a quiet place. it's a nice place -- just not the type of place a person goes to party.
I haven't been to Naxos, but it's also big with good connections.
Generally, in Greece, the rule is: if you want the best beaches, you need to go to the least explored islands (with no nightlife).