There are several publicly-available search engines devoted to think tanks and other public policy organizations and the most comprehensive is the following, which searches over 700 sites:
The following two resources appear to be comprehensive and authoritative lists of think tanks and similar groups.
The work of "think tanks" can provide valuable research on policy issues, but how interest-free is that work? Some nonprofit organizations are clearly advocacy groups, but others at least appear to be non-partisan. Two views: