If you're serious about staying local, then Rochester has options. A handful of decent beer pubs, a plethora of lager chav places and a nightclub that has a reputation for fights, loose women and zealous bouncers (think West Street followed by Barry Nobles Roxy in the mid Eighties).
If you're more discerning, then Whitstable is a cracker for atmosphere and pubs. You will find live music somewhere, it has two micropubs and you may get lucky with posh crumpet hen weekends staying in the old huts on the beach. No night clubs but two good curry houses. Canterbury is only 6 miles away and it has a couple of night clubs, though Summer months sees them quieter without the students being around. In August you may prefer to join the pretty young things with a barbecue and crates of beer on the beach.
As an alternative, Ramsgate has some great pubs that are a little down heel but with cracking variety of beer and atmosphere. The harbour has adjacent bars where local farming and foreign yachting types try to form mating relationships. Gets lively but friendly down there.
Me? I'd book one of Galvers micropub bus crawls. For thirty quid each he takes you to seven different micro pubs in East Kent. The cost covers the travel and a pint in each pub, how he does it no one knows, but you will see different parts of Kent, meet people and can end up in some nightclub in margate or ramsgate after. Its a unique way to do something different,
If you have other preferences let me know and I will make a suggestion.
Finally, you would regret staying in Gillingham, bad things really do happen to strangers there. A daylight only town for normal folk..