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Everything, IMHO.
1. Helsinki didn't impress me much personally; Lappeenranta is much more interesting, but as they say, taste is subjective. You need a passport and a visa for the trip, and the price of a one-day tour is very affordable – around 1,000 rubles.
It takes about 4 hours to get there; you can search for information yourself. Here's a link to bus tours as an example:
http://e-finland.ru/tour/type/bybus/
2. People will go there to have fun anyway; you can go with everyone, or if not, hire a taxi or take bus number 827. As for staying or renting accommodation, it's up to you. If you want to explore, do it; if not, rent a place.