Karelia is a border country that has changed hands more than once, and you can still see the seams. Sortavala belonged to Sweden, then to Russia, then to Finland, and was ceded to the Soviet Union after the Winter War of 1940 and again in 1944. Petrozavodsk began in 1703 as a cannon foundry for Peter the Great, and its name means Peter's factory. In between lie Lake Ladoga, the largest lake in Europe, and Lake Onega, forests, rocks and wooden churches that survived because nobody bothered to knock them down.
This is not a city break. The sights are far apart and the season decides what you get: in summer there are boats to the monastery island of Valaam and the wooden churches of Kizhi, in winter there is ice, snow and short days, and some things simply do not run. Five days is the right length for one clean loop, with two bases about 250 km apart: Sortavala for the marble canyon and Lake Ladoga, then Petrozavodsk for Lake Onega, a waterfall, Peter the Great's first spa and Kizhi. The same loop works from Saint Petersburg by train in both directions.
Days one and two are Sortavala and Ruskeala, day three is the train across to Petrozavodsk, day four a long day out to Martsialnye Vody and Kivach, and day five is Kizhi, with a plan B when the lake will not take you there. Start on a Wednesday: the Petrozavodsk museum and the Martsialnye Vody museum are closed on Mondays, and this order puts the museums on a Friday and a Saturday and Kizhi on the Sunday. The practical tips at the end are blunt about visas, cards and government advice, and for the country as a whole see Russia. A longer city stay in Saint Petersburg fits before or after: see 5 Days in Saint Petersburg.