I know this is a little outdated, but I thought I'd respond anyway, for future reference.
I have begun parking near Uwajimaya and walking down to Safeco field -- it's a little bit of a walk, but I enjoy stretching my legs before and after the game, and the parking is usually a lot easier to find.
On a different note: I would also recommend stopping into Shanghai Gardens for dinner before or after the game -- the most delicious Chinese food in the city, I think. My boyfriend and I are regular customers of the restuarant -- we even have a regular order.
My favorites on the menu include their hand-shaven barley green noodles (I prefer the beef or chicken chow mein), the moo-shoo pork (I don't think I'm spelling that right), their beef with broccoli, the pea vines (a must try if you've never had them), and the mushroom soup, although everything is great.
I especially like the fact that, if you stop by the restuarant late in the day, the kitchen and wait staff sit and enjoy dinner that they prepared in the kitchen together -- if the staff eats the food, too, it has to be good!