If you feel safe leaving your car at a light rail parking spot, you might consider that. I don't know how backed up it is when the game ends.
I went to the game last Saturday and sprang $12 to park at indoor parking on 7th St. and Washington. At the end of the game, I got out pretty quickly. The entrance is on Washington west of 7th St.
Up until not too long ago, you could find a free spot past meter hours on Monroe Street about 4-6 blocks from Chase Field, but now the meters are 24-7.
There is also a garage south of the ballpark off 7th St. and connected by a walkway, but I prefer the one I mentioned on Washington.