Well I live here, but I guess I know too much to have easy answers. I'll just flood you with information until I'm bored
Couple of good choices are definitely hitting some rock bars, since that's something we have plenty of. For example try heavy metal karaoke, that's not something you get everywhere.
Helsinki is also a very good place to eat well right now, as the quality places are very reasonably priced. The cheap/mid-price food on the other hand are IMO mostly overpriced, so I'd recommend spending that extra cash at least once for some fine dining. Especially if you're going with a girl
For example you can get a Finnish-style three-course meal for 39 euros at Ateljé Finne, which is a very good deal since the food is good. (Just don't ask the waiters for wine recommendations, get the owner or pick yourself.) Juuri has pretty much the same price range and quality of food, with possibly slightly more modern/cross-kitchen touch. (These are just a couple of options, there's really quite a few good places, I can give a whole list if you feel like it.)
There are also a couple of good budget options, most mentionably New Bamboo Center, which is a Malesian place. They serve great curry for what is a very reasonable price for Helsinki (around 8-9 euros I think these days). Asian buffets are generally of good value here.
As to drinking, that of course depends heavily on what you're looking for. The metal bars are mostly places for some relaxation beer or ten, easygoing, not necessarily the most social places. There are some more club-like rock bars, On the Rocks and Dante's Highlight, which are also less of metal-head places, for better and worse (mostly for the worse if you ask me). Oh and Bar Bäkkäri, which is big and relatively new and I know very little about it.
For some hipster moods you could try for example Kuudes Linja or LeBonk. Bar Loose is the definitive place for some alternative/rock people, although that doesn't necessarily say that much about the place. Anyway it's a nice bar, quite popular and one of the very few options here if you want your rock with little less metal. Tavastia is legendary, although it's for the tradition and quality of live music, it's nothing special as a drinking spot. Good DJ's usually though. Same goes for Semifinal (which is a part of Tavastia), which is a great place if you're the kind of people who like to go check out something cheap and obscure.
For some more popular-yet-trendy places, you could try Jenny Woo, The Circus or Teatteri (for a 25+ crowd).
If you're just looking for a nice selection and a nice atmosphere, I'd say there's tons of choices. Pub Amsterdam for example, Kaisla, William K's (there's several)... Really quite a good selection. Molly Malone's is a relatively old Irish pub with live music just about every night, for better or worse. It has a nice terrace. Everything is expensive though, but that's Finland for you.
If you're looking for a really Finnish experience without caring about the quality of music, there's places like Pataässä (a legendary/notorious karaoke-dump), Zetor (kitch/parody version of countryside nostalgia), Rymy-Eetu (semi-german) and Kaarle XII (horrible music, but plenty of dancing). Huuma is propably the most generic Finnish party-place you can find, which is not a compliment but it does give you a picture of a stereotypical popular drinking spot in Finland (although it's bigger than most). For the best guarantees of other people dancing, other than Kaarle XII you could check out bar Lost&Found (legendary for it's small and crappy dance floor, but there's usually some dancing even on the weekdays) or if you're the openminded sort, Don't Tell Mama (a hetero-friendly gay bar, guaranteed dance music). Lost&Found and DTM are both at Iso Roobertinkatu (or Iso Roba as people call it), which has about six other bars too in the two block walk, many of them good places.
Hotels I know much less about obviously, since I live here
The selection is typicly Finnish, which means it's hard to find anything cheap, but for 80-100 euros you can sleep in as close to the center as you like in clean and decent rooms. Book well in advance, Helsinki is a popular congress city.
Omenahotels can be quite cheap (there's several, you book through a website), but it depends a lot on the day. There's zero service (not even a reception), but the I understand the rooms are new, nice (in a slightly sterile way) and clean, so they can be very good value. They're all nicely located, very close to each other.
The hostels are clean and okay too I hear, although not that cheap (compared to hostes in other parts of Europe). Eurohostel for example is quite popular, I guess it's okay.
There's two hotels within walking distance of the Hartwall Areena (where they play the game), Sokos Hotel Pasila and Holiday Inn Messukeskus. Neither is anything special, and a couple of kilometers from the city center.
Now, sightseeing... Suomenlinna is nice, although it depends somewhat on the weather. It's a short and cheap ferry trip and a big sea fortress at the other end. If you feel like spending the money and the weather is nice, take a sightseeing boat. Finland has the most islands in the world, thousands of small islands all across the coastline, including Helsinki. It's very unique and some people like it a lot. I hear the National museum is nice and informative, although it's been ages since I've been there. I don't recommend the zoo, you can find better ones anywhere.
The Mannerheim-museum is pretty cool if less known place (most people from Helsinki propably haven't gone there). It has it's own webpage (in English too).
Check out Senate square for my favourite church in the world (although being an atheist, I rarely go inside)
One of my favourite walks is around the Töölönlahti (Töölö-bay). It has some nice old villas on the other side and it's just very nice and relaxing and very central, which is cool.
Hmm, is that long enough now? I guess.
But hey, you always ask if you think of something specific, I mean I could go on, and on...
Helsinki
