You will want a rental FOR SURE.
As for where to stay, if you're going to be driving to the site a lot, Seattle is out of the question. It's much longer than a 30 minute drive.
Depending on your budget, there are some decent places in Tacoma. Since I live so close, I have only stayed in a Tacoma hotel once. I chose the Hotel Murano for the occasion. It was pretty nice, much better than I expected, being in Tacoma.
If you decide to stay in Gig Harbor, there are good number of bed and breakfasts there... Could be another option. It would save you from crossing the Narrows bridge 100 times (it's a toll bridge).
As far as things to do/see...
The obvious are:
Pikes Place Market
Space Needle
Seattle Art Museum
The big ferris wheel that Icannot remember the name of.
The Aquarium (you won't be impressed, the 2.5 yr old will like it though.)
Maybe take a ride on, "The Duck" if you're goofy.
In Tacoma there's not a whole lot... DO NOT go to the art/glass museum.
Point Defiance Zoo (and small aquarium)
LeMay car museum (if you're a car person, it's pretty neat)
There is decent food in Tacoma
A few good breweries (that will allow the little one)
Harmon Brewery is very good. They have a sweet fish and chips deal on Sundays.
The Ram on Ruston is pretty neat. It has Washington's tallest bar, and waterfront seating.
Stanley and Seaforts is awesome if you want a NICE meal. Make sure to eat there at night though. The view from it's hill top location is beautiful. Probably not the best place for a kid though. Good wine selection, great steaks, nice place.
The Pacific Grill is VERY good if you can ditch the little on for a night, treat your lady to a nice dinner. Very solid Happy Hour as well. It's a nice place, but not as nice as Stanley's,
The Social is a good place... Sweet Potato Fries to die for.
If you're a pizza fan, Farelli's has good wood fire pizza. Also very family friendly.
Let me know if you have any more specific questions... If I were home I'd try to meet up..