I am looking for a site that will allow you to put in certain search
criteria so that you can look for an ideal city to live in.

Dear Ames, 

Here are several: 

The CNN/Money site has a place where you could see a survey of the
"Best Places to Live" in the United States.
Best Places to Live
<http://money.cnn.com/best/bplive/>    

Best Places.net 
<http://www.bestplaces.net/> 

MSN - Compare Cities
<http://houseandhome.msn.com/pickaplace/comparecities.aspx> 
Based on the abovementioned site (bestplaces.net), and could give you
a cost of living comparison.

CityRating
<http://www.cityrating.com/> 

Find Yourself a Spot
<http://www.findyourspot.com/> 

I hope this answers your question. Please contact me if you need any
further clarification on this answer.

Search "best places".