This place used to be the official easternmost point of the European Union but I think nowadays there is some argument between Finland and Cyprus about it... Anyway, the place is nice and in the middle of nowhere :)
The Warrior's House in Hattuvaara in Ilomantsi is a small but interesting place for those who are interested in war history. There is a little museum and also restaurant & accommodation services.
It is quite rare to see bears even in eastern Finland, but your never know. Finnish bears are usually peaceful guys and run away from you but please try to avoid those ones with babies :)