You are downtown, but on the periphery, which means that you're not super-close to anything or really far from anything.
You can stay downtown as pointed above, and walk to the market, or possibly Belltown (north of the market).
You can hike up to Capitol Hill, where there's a bowling alley/billiard bar (the Garage) that by virtue of its size alone, should have space. Alternatively, there are many, many, other bars in that neighborhood, too many to list here. Compared to the market, the hill is the same distance as the crow flies, but it's a climb.
You could walk or take the streetcar to South Lake Union and try out the Brave Horse Tavern, which is pretty great. But that might be one of the more crowded establishments around.
The fact that you are far from Pioneer Square (where the stadiums are) probably works in your favor.