Russia Anyone?

I am planning a visit to Russia in late summer or early autumn. But... it seems that getting a visa is more complicated than I have imagined.

For example I have been told by a Russian speaking lady from the Embassy that I will need invitation that can come from either Russian citizen or Russian travel agency.

I do not know anyone in Russia and I do not want to travel with agency like the flocks of tourists invading the cities (I'd hate it). My idea is just to go there and decide on the moment where to stay or where to go.

Have you traveled to Russian independently? Any ideas for St. Petersburg region?