What kind of fun are you looking for? The Washington State History Museum is great, the Tacoma Art Museum frequently manages to get good traveling exhibits (though it's been too long for me to remember what their permanent collection is like). Pacific Avenue has a lot of shopping, antique stores, etc. There are some seemingly nice restaurants down there (including an El Gaucho), but most I've not been to so can't specifically recommend. There's a place at the north end of the main stretch of Pacific called Meconi's which is a cool little room that has good pub grub and a great beer selection- though it's more of a hanging out earlier/happy hour/mellow place than a going out for the night joint. The Swiss, up on Jefferson, was where I cut my drinking teeth, from 1998-2002. Haven't been there for about a year, but it's still friendly, it's in a huge old industrial building, a real bar-type bar, with free pool every Sunday and Tuesday on their full-size tables- avoid it on Friday/Saturday, unless you want to hear some shitty cover bands and enjoy more of a late-thirties/forty-something pick up joint vibe. Head next door to The Rock for decent pizza, etc.; it's a bit more of a chain now- still local- but I think this was the first one. (Previously called "Rock Pasta", we used to head over here on break from playing pool to take a quick shot before The Swiss got hard liquor.)
The two bars everyone goes to are The Corner Bar, which most Tacoma people still refer to at least half the time as "Hank's", which it was for a really long time. It's a very unassuming place with an interior that kinda says "portable classroom" to me, but they're really friendly, good beers, a couple of pool tables, and like I said, everyone hangs out there. The other one is Magoo's, which has more of a old school bar look to it, but get there on the earlier side of late or there won't be anywhere to sit, and it's not the most comfortable room to stand in. There are a lot of UPS kids who hang out here, but there's a decent spectrum of people, and anyway, UPS joints aren't like UW joints.
Puget Sound Pizza is a kinda cool, underground room- a lot of my Tacoma people were spending a lot of time there a couple of years ago. They used to have a lot of karaoke, though a quick glance at their Myspace page, as well as a Yelp search didn't reveal one way or the other, so I'd call. Down the street from there is an "Irish" bar called Doyle's that's pretty nice and recently was included on Esquire Magazine's "Best Bars in America", for whatever that's worth. I know they have some kind of cable package- or used to- because for a while my brother was going there to watch all the international soccer games. And another place that Esquire likes is The Parkway, which I never used to hang out at because it was non-smoking and my friends and I were little twenty-something chimneys, but they have a great beer selection, and I think it's a mellower kind of thirties-plus-ish place, for real beer-lovers.
If you go up Sixth Avenue, there are a lot of other little bars and restaurants. O'Malley's is a nice bar-type bar, with karaoke a couple of nights a week, and Jazzbones and Hell's Kitchen both have a lot of live music- local as well as touring acts, the former having previously been almost exclusively jazz and blues, the latter metal and crusty punk, but both have branched far, far out in the last few years. Sixth Ave. is also home to a lot of little shops of various kinds. Don't know if they've kept the quality up, but Gateway to India used to have about the best Indian food around- actually better than most I've had in Seattle- and it's a nice, friendly little joint- clean and comfortable enough for a casual date. Full disclosure: it's been a few years. Proceed with caution. Follow Sixth all the way to the west end and check out Titlow Beach.
If you're there during the day you should definitely check out Point Defiance, which is unlike anything I've seen in any other city. Think if Discovery Park was easier to drive around in, had a lot more trails, and instead of a military base, it had Woodland Park. You can take a nice stroll in the woods, go down to the water (Owens Beach is not the greatest beach ever, but many of the trails lead down to the water as well) , or check out the zoo and aquarium. Drive there along the Ruston Way route, along the waterfront, also home to some decent restaurants. The other neighborhood I could recommend for walking around is the Proctor District, which is a collection of nice little shops, although be warned that it's a little...bourgeois, I guess: a lot of knick-knacky type of places, antiques, home furnishing, etc. But it's still a decent neighborhood.
That should get you started, anyway. At least get you a beer or two.