Dont't miss Temppeliaukio (Rock Church). It's built up in a rock and looks amazing inside, while from outside it's just a pile of stones and you would never say there's a church or anything else inside. Beautiful!
Helsinki is the capital and largest city in Finland. It is also one of the main points of entry to the country (Tampere and Turku are the others). It is home to the University of Helsinki (the biggest university in Finland) and the Sibelius Academy (the only musical university in Finland and one of the biggest in Europe), and it is definitely at its best in summertime.
Your choice of Helsinki hostels is plentiful but they tend to be pretty separated from each other. Finland is also generally a pretty expensive country to travel through, so expect to pay at least 20€ a night for your stay. Regardless, hostels in Helsinki are definitely the most economical lodgings for a budget traveler.
While staying in a Helsinki hostel you'll want to see Suomenlinna (roughly translates as "Castle of Finland"), which was built in the 1700's. The archipelago around Helsinki is also beautiful and definitely worth visiting. There are also plenty of parks, museums, churches, and galleries for those interested. For the thrill-hungry, Linnanmäki (the oldest amusement park in Finland) is the place to go.
If you're into soccer or football, you can catch a game at Finnair Stadion. There are also two ice hockey arenas in Helsinki, both home to a Finnish main league ice hockey team. Hartwall Arena (one of them) is the biggest indoor arena in Finland. It's useful to check their schedule, as the arena is often used for big musical events.
For moving around the city, trams are your best bet, but there are also networks of buses and trains you can use which makes the city open and convenient no matter what Helsinki hostel you stay in. The whole public transportation network in Helsinki is coordinated by the same company, so when you buy a ticket from them, you can use it to gain access to almost all the public transport options in the city. The ticket prices start from 1.8€. You can also access other interesting places in Finland through Helsinki, for example Hanko (the southernmost point of Finland).
Helsinki's climate ranges from freezing cold in the winter (over -30 degrees Celsius) to considerably warm in the summertime (over +25C).
Helsinki is generally a very safe city to visit, but use of common sense is still advisable, especially in the nighttime.