Seattle Mariners pub crawl
Between the convention center and Safeco, the Elysian Fields (1st ave S a few blocks north of Safeco - also has an entrance on Occidental Ave S.) brewpub probably has the best beer and food - the food's a bit on the pricey side outside the happy hour $4 mussels and $2 truffle fries, but definitely a cut above the usual pub grub. Worth a stop for their beers, if nothing else. I'm a big fan of their amber and ESB - they have a pretty good Maibock on right now too. This place also has the big advantage of size. It's *huge* which means that even on a Mariners gameday or a Friday night you can get a drink and a seat if you're so inclined. (Forget about Seahawks gamedays, though; it abuts the Qwest Field north parking lot)
Other stops you might consider, depending on the atmosphere you're looking for:
Fado on 1st and Columbia has the best Guinness in town. Food has gone a bit downhill of late. There's another Irish pub on the back side of the same block called the Owl & Thistle, but I've never really dug it.
Just north of Fado on 1st Ave (I initially mis-remembered it as being south of Fado) there's a place called Contour that's a bit funky. It's a dance club at night (very popular with the local Russian community, it seems), but from 4-8 they have a respectable Happy Hour that includes $2 pints of "Driftwood Ale" (actually a renamed Rogue Half-a-Weizen) and cheap appetizers of varying quality. Avoid the $2 burger - it won't make you sick, it just doesn't taste very good. The calimari is ok as are the various meats-on-sticks (kebabs, skewers, whatever they're called.)
The J&M bar on 1st and Washington is an atmospheric kind of place during the day. I've had a decent burger here before. It's not such a great place at night when it turns into a pioneer square meat market. Beer selection is par for the area (which is to say decent).
The Collins Pub (2nd ave btw James & Yesler) has a very good rotating beer selection and decent food. I'd put this second behind Elysian for beer and food.
The place next door to Elysian, Sluggers, is a pretty generic sports bar with an okay cheesesteak that'll be less expensive than anything at Elysian. You can get pitchers of Mac & Jack's African Amber (a local brew that's only available on tap, not bottled or in stores) here at least.
Finally, the Pyramid "beer garden" (aka, temporarily-fenced-in parking lot) next to Safeco is a good place to put away some last-minute hefeweizen. (I think Pyramid's hef is the best.)
Inside Safeco, there's actually some really good beer to be had. Most stands selling beer will have a rotating micro tap or two - and they vary from stand to stand. You'll pay though ($8.25, iirc). Good garlic fries in there, too. The pub on the bottom level by the visitor's bullpen has a killer pork sandwich.
Hope this helps.
(addendum - my favorite bar in the downtown area, the Two Bells, definitely has the best burger in town, good beer, and a great vibe. It is, unfortunately, well north of the convention center, meaning it's something like 2 miles north of Safeco. But it's just a great bar, comfortable like an old pair of shoes.)