It is my hometown. It is unlikely you will be able to fly in directly to Petrozavodsk airport. You will need to go through Mowsow or St. Petersburg, then take an overnight 12 hour train. It is a charming city with parks, gorgeous lake Onega and deep forests around. there is not much to do in Petrozavodsk itself. Be sure to take a boat (6 hours) to see Kizhi.
The city is simply terrible, there is no infrastructure, some are “beautiful”, but, again, paid places are far away, there are no buses to go, I had to rent a car ... The roads in the city are terrible, there are no views, in general, if you saw a lot of beautiful photos on the Internet about Karelia, then go and check, it’s not worth it
Very cozy and friendly city!)))