Yeah, don't meet strangers and get too friendly with them if you know what I mean. Go with a buddy if you are going out during the night time. Make sure you don't drink and drive. Wear your seatbelt at all times whether you are driving 5 milies an hour or 100 miles an hour. Be careful with whom you associate with. And stay away from drugs!!

Come to Weihai instead, I'll show you lots of awesome places to eat dumplings and drink alcohol!

Anyways, my Shandonger friends have told me that there's a fountain in Qingdao from which everyone drinks the water. I suggest that you do not drink water from said fountain.

If you are into beer (and large crowds since it will be a national holiday) you might want to visit the Qingdao brewery.  The beer they serve in the brewing room at the end of the tour is actually very good.

There's a cherry blossom festival around this time of year.  I'm not sure if it happened yet.  It's a beautiful display of nature in the park.  Check them out if they're still in bloom.

Stay in Ba Da guan!

I'd recommend checking out the old stone man beach, as it's (slightly) cleaner and larger than any of the other ones in the city, though it will probably still be too cold to go swimming. 石老人海水浴场. 

Mount Laoshan is worth climbing as well, but is located somewhat far away from the city center. 崂山.

The May 4th square in downtown is pretty cool too. 五四广场

Also, head to the old (German?) part of town and stroll through some old hutong-esque alleys. There's pretty decent seafood down there too 青岛古城.

Some good advice above.  I'll add a few embellishments.

I'd visit Badaguan, the old German enclave in the west end of the city.  It's a nice walking neighborhood along tree-lined streets and dilapidated, but still interesting Germanic architecture.

Take a seaside stroll along the on-and-off boardwalk starting at the International Marina (next to the Intercontinental Hotel) and proceed west, until you run out of footpath.  Hope for a sunny day with little wind.

Visit the Tsingdao Beer brewery for a bit of local color, history and grog.

Coffee Street (Mingjiang Lu Number 2) is coffeehouse after another.  If the weather is nice, some sidewalk cafe action.  Good for people watching or immersing yourself in a book & a cuppa.

Most laid-back bar in the city is Old Jacks on Yanerdao Lu.  Old Jack is often found practicing classical guitar in the joint, a joint that comes closest to your friendly neighborhood tavern back home in the West, and the gin & tonic is reputed to be the best in town.  His coffee is also highly rated.

Lots of good good Chinese seafood restos.  I'd stay away from the Western restos, though.  Overpriced, overrated and crass imitations of the Real McCoy, except for...

The Kiwi Cafe in Hong Kong Garden. The proprietor is a Chinese bloke called Danny, a repatriate from NZed who does all the cooking: lamb, blue cod, eggs benedict, u-name-it, etc. and the Kiwi is the only place in town you can get a bottle of authentic VB (Victoria Bitter) from Australia.

If you want culture, i.e. traditional/modern, Chinese/Western, go to Beijing or Shanghai. 

Have fun!