how lively are you looking for?
you could opt for the capital las palmas, or if a beach is more important then you may be better off going to a hotel somewhere in playa del ingles which is a very popular beach and has good nightlife in the area too. depends on how young you are and how much you like your nightlife - there are some great clubs there!
The good thing about gran canaria and the canary islands is the weather - it's usually mild and I would expect temperatures between 19-24 degrees I would think? I've been to the canaries before in October and the weather was lovely.