The admission age varies from bar to bar. It ranges from 18 to 23. Most places check for ID at the door, and if you're much too young, they won't let you in.
Cover and drinks can be expensive, depending on the bar. In some places, cover can be as high as 70-80 SEK and drinks as expensive as 50-60 SEK each. Also, since there are so many people waiting for drinks at the bar, it can take a while before the bartender gets to you.
Unique Suggestions: If you get asked for ID but you know you're too young, you might be able to get in by saying you forgot your ID. Also, if you're with a big group of people, they might just ask the first person for ID and let the rest of the group in.
If you drink in the bars, you can try having a "pot" where each person in the group gives one person the same amount of money each (100 SEK is what we usually used in my group), and that person goes to the bar to get the drinks. That way, everyone gets their drink at once, and there's less time waiting for the bartender. Also, it usually ends up being cheaper, especially if you like drinking a lot on a night out. If you're only planning on having one or two drinks, buy them yourself, but if you're planning on having more, putting money in the "pot" is cheaper.
Fun Alternatives: If you get ID-ed and get rejected, just go to another bar and try again another time.
Instead of buying your drinks at the clubs, try hosting or going to a pre-party and doing most of your drinking there. Alcohol from the Systembolaget is cheaper than in the bars, and pre-parties are always fun. If you've already done most of your drinking at a pre-party, you'll likely end up buying less drinks at the bars.
There is a tourist office downtown, in the main square. It's a good place to get information and to buy souvenirs, but a lot of the souvenirs they have there aren't as authentic as the things you'd find in Anna's Bod (another souvenir shop in town).
Unique Suggestions: Don't spend all your souvenir money there!
Fun Alternatives: Check out the other little souvenir shops in town. They're less obviously targetted towards foreigners. Anna's Bod also offers free gift-wrapping!