How would I find out the strength of the economy in any city or region in the U.S.?

Question

Is there a list that would compare the major cities? Is there a database somewhere?

Answer 1

Each U.S. state records its GSP (Gross State Product)

For cities, look for GMP (Gross Metropolitan Product)

You could also look up (or just compare and make your own) growth / decline rates for the GSPs and GMPs.