Whether you have a day or a week in the area, there are lots of great things to do in Tacoma and the surrounding area.
Just a short drive from Tacoma is Wild Waves and Enchanted Village, a theme park/water park, fun for the whole family on a hot August day. Pack your sunblock and get ready for some great water slides.
The Tacoma Rainiers are the AAA feeder team for the Mariners. If you want an evening of seemingly-small town baseball, head over the Cheney Stadium for a game. The Rainiers will be playing the Albuquerque Isotopes on Wednesday and Thursday before the wedding, then they head out of town.
The Point Defiance Zoo & Aquarium is located the same park where the wedding is taking place. This zoo is little in a good way--as in, it's possible to see everything without getting overwhelmed. The zoo specializes in animals from the Pacific Rim. (Also, you can visit sister Tracie who works in the gift shop!)
The Museum of Glass in Downtown Tacoma has a gallery with rotating exhibits of glass art, and the hot shop (that silver cone you'll see in pretty much every picture of downtown) is great--people blowing glass all day long! If going into the museum isn't your thing, you can still check out the Bridge of Glass, a foot bridge with lots of glass art on display to the public, and the outdoor plazas of the museum for free.
The Washington State History Museum. It's about the history of Washington. Fun for kids.
The Tacoma Art Museum specializes in showcasing Northwest art. Located within walking distance from the other two museums.
Important note: All three museums have free entry on the third Thursday of every month, which happens to be day before our wedding.
That's our short list. TripAdvisor has lots of other ideas.