I think the better way of getting accurate details for your site or domain is by the following steps :-
If you are using a general purpose search i.e. not intended to any specific group of visitors - You can safely use Alexa traffic Ranking for it. Also you can see how many back links pointing to your site.
If you using keyword specific/ visitor specific then try to use the freely available tools on the web that analyzes traffic based on specific keywords. By that way you can know what kind of visitors you are actually getting...