Street addresses or village names could be a good beginning for looking through church records. The name of an office or factory, with the date of departure from this job, yields your ancestor's file from personnel departments that keep such records almost indefinitely.
Dates are of special importance.
Without exact names, locations and dates no archive is going to help you. Postings on various on-line billboards remain a possibility, but the Russian net is still in a nascent state, and the number of people with the WWW access is too small to hope that such ads produce tangible results. Nevertheless, I know of several cases of BBS announcements that have actually ended in finding ancestors. The key factor of success was either a very rare surname or one belonging to a famous family. If you have the basic data ready, the best way for a foreigner would be to retain a reliable contact in Russia.