United Planet (www,unitedplanet.org) is an organization that offers volunteer placement in some 40 countries around the world. From one week to one year, the tasks include teaching, improving the environment, working with women, disabled people or animals, or working in orphanages.
The opportunities are not cheap, but for the longer placements they can be quite reasonable on a per day basis. A one-week placement starts at $995, while a six-month arrngement goes for $7965. The six-month fee works out to about $45 a day.
These prices include food and lodging, airport transfers and medical insurance, but not air fare or visas. Program fees are tax deductible for U.S. taxpayers.
I checked out the possibilities in Russia, which require at least a six-month stay. You can work with people with disabilities, with veterans, the poor or the elderly, or in a cultutal centre. Based on the map shown, the placements seem to be in Novosibirsk, which would be a great place to work on your Russian language skills. It is far from Moscow (and just about everywhere else) and its suburb Akademgorodok was one of the jewels of Soviet-era science.