Well I asked my brother in law that lives in Tacoma for some advice on hotels and here is what he gave me, which is more than I expected. I imagine I may owe him a beer or two after this event actually takes place.
I imagine being in downtown both has appeal especially because it would put you close to LeMay: America's Car Museum. There are a number of hotels that aren't too far away. These are not necessarily in order of your best bet:
1) La Quinta: Pretty close to the Tacoma Dome. The price will probably be about right, though the neighborhood there starts getting a bit of the "spotty" side.
2) Marriott Courtyard in downtown Tacoma. As it is downtown, the price will certainly go up a bit, but they have plenty of access to garage parking that should be pretty secure. The Marriott is right next to the Convention Center
3) Hotel Murano is going to be on the high end expensive side. It used to be a Sheraton, but they redid it a number of years ago and it now has a modern art vibe with lots of glass art in particular. The Marriott and Murano are in great locations downtown where there would be tons of restaurants and museums within walking distance.
4) The Puyallup tribe runs a hotel linked in with the Emerald Queen casino just north of downtown and right off to the west of I-5. To be honest, I haven't been there but I believe they took over a Best Western. They have lots of entertainment that rolls through there and their own restaurant, though being there might limit access somewhat to restaurants other than the ones they have on site.
5) There is a Silver Cloud Inn on the Tacoma waterfront, but the issue there I suspect would be parking. I can't remember if they have their own parking garage. The location is amazing and folks would be within walking distance of a bunch of great restaurants on the water and up the hill off the water as well.
6) There is a Shilo Inn further south from downtown that will probably have pretty good rates and reasonable proxity to restaurants. It is right off of I-5. The location is kind of in an area rife with strip malls and close to the Tacoma Mall, so lacks the "cool" factor of downtown, but I suspect rates are much more reasonable. I think there is also a Holiday Inn Express and Suites really close to the Shilo as well. The Shilo has been around for a long time, but I think the Holiday Inn is relatively new. There might be a couple of other hotels there (Comfort Inn) too.
I would recommend starting with the Courtyard Marriott downtown. It might be pushing the upper limit of what you are looking for cost-wise and just about any downtown place will have an additional charge for parking, but it is probably the best location you could ask for. There are some hotels close to Tacoma Mall like the Hampton Inn that might be in your price range, but once you start getting out where the mall is car safety might become a major concern.
So what does everyone think? Marriott sounds good, but it will be spendy. I just checked for a price quote around our proposed July date and it was $200+/night. I would hope we could get a reduced group rate, but not sure. John (Vman73) is checking on a Best Western in his neck of the woods (just across a bridge from Tacoma) which may produce a better price.