One thing you might do before the game is go to the Pioneer Square underground tour. You can find it doing a search on the net. Very popular and very interesting, and it is located fairly close to the baseball stadium. I think tours start early in the morning, like 10 or 11, so you could easily do that before the game (I think probably an afternoon game?) The new stadium is amazing itself--plan to go early to the stadium to be able to tour around.
Hope that is a good suggestion for you!