For the game you're basically restricted to Bristol Beer Factory or Tobacco Factory as others have mentioned. If the weather is nice you can just grab some drinks and chill in the park behind the ground, loads of locals do the same on a nice day.
Afterwards I would head back into town via The Orchard on Spike Island, it's a proper cider boozer, get some local scrumpies and set you away.
From there I would do one of the following:
Floating Harbour crawl - The Cottage, The Pump House, The Grain Barge, The Ostrich, The Louisiana.
The Old Town - loads of bars including games bars, cocktail bars and late night places. Near St Nicks Market as TD said.
Gloucester Road - Start at the bottom of Stokes Croft at the Full Moon then work your way as far up as you can handle. Dozens of places.
Clifton Village - Bit of a fancier vibe if that's for you, nice few cocktail bars and go to The White Lion beer garden for great views over the suspension bridge.
Clifton Triangle/Park Street - more studenty but tonnes of bars.
North Street - should be open after the game and you can slowly make your way back to town.
King Street - Start at The Apple, a cider bar on a boat, then make your way down the Georgian pedestrianised street that has about 10 places to drink.
Bristol can keep your average boozer busy for years.