There are multiple companies running routes between Stockholm and Turku or Helsinki, as well as Helsinki and Tallinn, and they can be fairly cheap to use. It really just is a matter of improving the connections, if you want people to be able to continue on to other European cities. A tunnel or a bridge would be ideal, but they are a big investment and you can make it work without.

I used to travel from Denmark to Åland (between Finland and Sweden) and back a couple of times a year as a child, and have also occasionally continued on to the Finish mainland. The train ride though Sweden is not bad and neither is the boat ride, but having to use three different ticketing systems, making sure you have enough but not too much time, and just that you know where to go and have your tickets in order, can be.