The most inexpensive way to see many of the main sights of Helsinki is to hop on Tram 3T (or 3B, which has the same route but in opposite direction). It is also very convenient - during the day time, you won't have to wait for more than 7 to 10 minutes at any stop for the next tram. So you can spend a few hours hopping on and off, to see much of Helsinki. Or, you can just ride the full circle without stepping out, if youre feeling lazy!

In the pictures below, you will first see the route map for the tram (I scanned this map ... (more)