You should get there as early as possible. Even though this garage is not right at the Tacoma Dome, it is walking distance and cheaper than parking in the lots at the Dome. If you can get there 90 min to 2 hours before, you "should" be able to get a spot.
The roads in and out of the parking garage are tight and crowded with commuters trying to leave and concert-goers arriving. Freight House Square, across the street (you'll pass it on the walk to the dome), has a large food court. It's old school, but has good options. So if you come early, you can park and eat before heading up hill to the dome. As I said, though, the lot has commuter cars parked too. They start leaving around 3:30 as the trains arrive from Seattle every 20 minutes or so, so it empties out, but creates some gridlock.
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