I live near Tacoma, so here are a few of my favorite frugal things to do. For the outdoor things, it will be rainy and chilly (generally 40s), so pack good rain gear.
Point Defiance Park has nice hiking trails with gorgeous views of the water. Well groomed, flat trails through thick forests, and you can follow the trails for either an easy 1 mile hike or an easy 5 mile hike. There is a bus that drops you off or there is plenty of parking at various points on the trail. Also at Point Defiance is the zoo with the zoo lights - it's a bit expensive ($17?) but you can spend hours there.
6th Avenue is cute and has some fun shops. Downtown Tacoma on Pacific Avenue, by the University of Washington-Tacoma, has a row of great, unique shops and restaurants. It's also right by by the History Museum and the Museum of Glass.
Over in University Place (about 6 miles from Downtown Tacoma) is a nice park called Chambers Bay. It has a 3 mile, paved walking loop with just amazing views. It's built on an old rock quarry and there are cool "ruins" to explore.
Another fun activity is to walk across the Narrows bridge. You can park at the War Memorial off 6th avenue and walk through the park, then take a walking path to the bridge. It's pretty cool. If you drive across the bridge, there's a toll to return. Walking is free.
Tacoma Community College is off 19th street and has a few galleries open to the public, with rotating student art shows. Just a block away is a place called Pint Defiance, with a variety of microbrews on tap and a huge variety of local beers to buy. There's also a rollerskating ring next door.
You can easily catch the Sounder train at the Tacoma Dome station to Seattle, and then ride it back - but it runs commuting hours, like 6 am departure and 5 pm returns. Still, it's a really cheap and easy way to get to downtown seattle for a day trip. There's also the 590/594 express buses that run all day from the Tacoma Dome station. I'd use a bus instead of trying to deal with the traffic and parking.
A fun place to visit is Half-Price books. It's by the Tacoma Mall, and has a great variety of (1/2 priced) used books.
Hope that helps!