Hameenlinna fortress is in Southern Finland, just in the very center of the land of the Tavasts. The harsh people of Tavasta are the indigenous population of these remote and wild places.
Nevertheless, there are no problems getting there. You could drive to Helsingfors (Helsinki) along the third ring and then along the highway to Tammerfors (Tampere). You can take an electric train from the Central station in Helsingfors (Helsinki), which is somewhat faster, because sleep carefree all the way.
You can, of course, hitchhike, which will take much longer, because... hitchhiking in Finland is 'something special' (vote even before the 'poppy's curse' — nobody going to stop, I tried that kind of traveling on Suomi).