It's all subjective, but I would personally spend the most time in Helsinki. Just remember to bring a fat wallet with you. I think most people underestimate how expensive it is to do things like go out to a restaurant or grab a pint of beer in Finland. Taxes are extremely high, but as you'll see, they are put to very good use.
FOOD & DRINK RECOMMENDATIONS
Belge - Centrally located, they serve lots of excellent European food, with a few traditional Finnish dishes too. The atmosphere and interior design is also really cool.
Similarly, if you want to go for a really nice dinner and don't care about the cost, Restaurant Savoy is also right on the Esplanadi and serves some of the best (and most expensive) food in the city. High end dining for sure.
Konstan Möljä - If you're near the West Harbour definitely stop here for some classic Finnish food, the restaurant itself is dressed in a traditional Finnish style too. It's just a great experience for tourists I think, and most importantly the food is excellent.
- - -
As for drinks, there are a pleasing amount of brewpubs and unique watering holes there are to discover. Despite the high cost of alcohol, Finns still love to drink, and your chances of actually spending time with some locals are definitely much higher at a bar or pub, so for that reason you should probably spend an evening at a pub.
With that said, if you're just trying to get drunk with some people you've met at the hostel, I'd say skip bars and pubs and just stock up on booze from the Alko stores. It will still hurt the bank, but at least prices are slightly more reasonable than pubs.
- - -
OTHER RECOMMENDATIONS
Candy stores - just do yourself a favour and pick up some Finnish candy and/or licorice. It's soooo good. If you don't find yourself near an actual candy store, you can pop into any major cinema where they will have a huge wall of sweets to choose from. Just fill a bag and take it to the ticket counter to pay.
Moomins - if you don't know about Moomins, they're kind of a big deal in Finland and you should learn about them. There are tons of cute cafes and stores to check out that are Moomin themed, we had a blast spending an afternoon doing Moomin stuff.
Art and music - Helsinki surprisingly has a really cool art and music scene. We found it a bit difficult to find just by walking around, but if you look online you'll easily be able to find some small galleries or music venues to visit. If you like Metal music you'll be in for a treat.
Public parks - get out of the downtown core and walk through some of Helsinki's awesome parks. There are actually quite a few of them and they are all beautiful. I especially like the one that's also a graveyard... I can't remember the name right now, but it's pretty spooky.
Suomenlinna - I'm sure this has been mentioned already, but I think it's kind of obligatory to go to this sea fortress. Take the ferry, dress warm (the Baltic winds are cold), and get lost in the history.