Brighton's great, a really nice seaside town with good bars & places to eat/go out, it's been a couple of years since I was there but Kemp Town was a nice part of town
www.visitbrighton.com will give you plenty of ideas.
If you're keen to go to some sports then go to London, from Gatwick you should get the train to Victoria, there's normally some deals availible for rooms, try laterooms or lastminute.com I usually manage to get a deal of some kind.
Once in London there's the usual array of football grounds or for Rugby if you happen to be there for the weekend you could try Harlequins at the Stoop or Saracens at Watford (Season doesn't start until September 6th and there is the annual double header at Twickenham involving London Irish v Wasps & Quins v Saracens)
Otherwise Wimbledon Dogs is a good night out, Windosr has racing on a Monday night during the Summer months, other tracks local to London are Ascot, Epsom, Lingfield & Sandown Park.
As a wild stab in the dark if you are interested the Cricket season is coming to a climax, England play 2 x One dayers against the Proteas at the end of August but tickets may be hard to come by.
Last stab in the dark, the Tour of Britain road race starts in London on the 7th of September, it's no Tour de France though.