I will be staying in Kuopio for a month in July and I would like to know if there are any nearby cities worth visiting (even if by train or bus) whilst I'm there. Thank you.
You could take the lake cruise to Savonlinna
and a bus back.
A nice day trip would be a drive to South-East to Joensuu via Lintula and Valamo convents. Then tour around lake Pielinen visiting e.g. Koli, Lieksa, Nurmes. That would require a rental vehicle.
If for some reason you don't drive, Varkaus, Jyväskylä and Iisalmi should be easily accessible by public transport.