Start a "sister-city" petition.

There are a staggering number of sister cities to Russian cities, that could be included in the campaign to sever "sister-city" relationships. If you don't see your city at the bottom of this blog page, please consider checking to see if your city has any Russian connections.

http://en.wikipedia.org/wiki/List_of_sister_cities_in_the_United_States
or
http://en.wikipedia.org/wiki/List_of_twin_towns_and_sister_cities_in_Russia

Once you find a city you feel compelled to petition you could go here to start the petition.

https://www.change.org/campaigns/stand-up-for-lgbt-in-saint-petersburg-and-russia

or go to Moveon.org and start the petition there.

No matter where you start the petition, be sure to include the name of the Non-Russian city your petitioning in the title of the petition.

Malawi

This petition was successful:

http://www.change.org/en-GB/petitions/ask-rt-hon-theresa-may-immediately-stop-aid-to-malawi-after-new-law-passed-criminalizing-lesbians

Long Beach -//- Sochi

There's an article in a local paper about the Long Beach to Sochi "sister-city" petition:

http://www.lbpost.com/lgbt/2000002714-petition-calls-for-long-beach-to-dump-sochi-russia-as-sister-city#.UgqbfGTXhe4