This is just a curiosity to me. Is there a reasonable way to find out what queries put my site near the top of search results? I know it's not really a solvable problem, since there's an unlimited number of potential queries. And I could always search for a unique sentence copied from my site, and show up number one. But, for example, it would be neat if Google kept track of the top results for every query and let you search for your site against that.
If you frame your question slightly differently you can find a solution. Instead of asking "What keyword searches return your website closest to the top" instead try asking "What keyword searches that people use return your website closest to the top".
The second question is better because you shouldn't care about keywords that work well for your site but no one searches or is likely to search because it doesn't help your site.
In the case of the second question the easy answer is that you can get the results for the top ranking searches in Google from Google's Webmaster Tools. Just go into Your Site on the Web->Search Queries and sort by the Avg Position column and you will see what keywords people search that you are currently doing best at.