There are several places within walking distance of your hotel.
Near Santa Clara and San Pedro streets you've got The Tied House (tied to Redwood Coast Brewing Co), Britannia Arms (good selection of beers and british food, sometimes there is live music), and an Irish placed called O'Flaraty's (or something like that).
Near San Fernando and 2nd, you've got a Gordon Biersch brewery restaurant that has patio seating and a bar - this might be the original GB, not sure, San Jose Bar and Grill is really just a bar with a decent selection and is a popular place. Across the street is Caper's Loft which is a restaurant with a popular bar, not sure about the beer selection though and not so much of a pub atmosphere.
I can't think of any place that had Bear Republic brews on tap though. But at least this list can get you started.