This weekend, we are going to our first Mariner's game. I'd like to avoid as much of the traffic as possible, so I was thinking of going downtown early (Sunday). Are there things to do in the immediate area that would keep us (2 adults, 2 kids)occupied? Also, would there be a good lunch spot near by?
Thanks for your help!

Go to temple and pray they win a game!

The core of Seattle downtown is less than two miles from the ball park, and it is easy to catch a free bus MOST of the way to the ball park, or pay $1.25 for a ride on those same busses to the front of the park.

So, that allows you the entirety of Seattle downtown for your pre-game options.

Needless to say that anyone could find plenty to do and eat with that as your range.

On-street parking is free on Sundays too, so find a spot EARLY and then leave your car there all day... then either walk or take the bus back up town after the game.

You won't have any problems.

And the ball park is awesome!

Have you seen the new library (between 4th and 5th, Madison and Spring)? It's definitely worth a stop, and it's not a bad walk to the stadium (or, a free bus ride, like the other poster pointed out).
Walking through Pioneer Square and then along the waterfront (lunch at Ivar's Fish and Chips?) would be another idea. Again, I don't know that that counts as the immediate area, but it's an easy walk and with the waterfront trolley and the free buses, it's not out of the way.
Tat's Deli (an east coast style deli) at 115 Occidental S. would be a good pre-game place to eat-they're not normally open on Sundays, but are before baseball games. www.tatsdeli.com

Slam 3-4 Red Bull's to keep you awake!!

the weather should be really nice on Sunday also, I agree with the exploring the waterfront idea- the kids would probably really like the aquarium. Shopping at Pacific Place or exploring Pike Place Market are also fun things to do- lunch at the market is awesome! maybe have brunch (make reservations) at cafe campagne, yum!! or Etta's.

Pioneer square is walkable to the Safeco. As far as places to eat...save the eating for the great Garlic Fries at the Park! If you were looking for something to take home with you the Mariners store is huge and could occupy quite a bit of time if you are like me!