I'd check out the Dutch Trading Company or DTC bar. It is not too far from the city in Victoria Park.
Petition Bar in the city has just opened up with a good tap list. Not far from there is Bob's Bar on the top floor of Print Hall (where the West Australian Newspaper used to be printed). That's about it for bars.
For breweries, Feral and Homestead are quite close. The other Swan Valley breweries are pretty close to one another. Swan Valley is pretty unique, being a wine area so close to a major capital city.
Fremantle is interesting from a historical perspective with a good Maritime Museum and a lot of old buildings. The ferry to Rottnest Island is ok, but if strapped for time, i'd probably suggest seeing a Quokka for the first time isn't really worth it.
If sport is your thing...the Perth Wildcats are a successful basketball team (29 years in a row in the playoffs) and play at a new venue right in the city. Cricket has also started at the WACA ground, also right in the city. Australia is playing New Zealand in a Test Match (5 days) that you might just catch the end of. Otherwise there are domestic games also at that venue.
Margaret River wine region is about a 3 hour drive south of Perth and quite popular. A number of breweries are based in the region. Busselton is also down that way and is a nice beachside town.
If you want to meet up with any beer people, let me know, have a few friends over that way. Likewise, if you are looking to trade any beers, let me know.
Enjoy your trip and Australia.