Although the numbers are a bit elevated for todays market - zillow.com provides pop-up numbers on homes on their maps. You enter the address and the hybrid map shows you the neighborhood. You can even zoom in on your home - and see the prices for your neighbors.
A refi appraisal will be conducted by the lender - and typically they tend to be higher than an initial home loan. Don't ask me why - I'm not an appraiser - but since you are doing this for your own information - it would be a good resource for you.
Keep in mind, as I said, the refi lender will do their own - and base their numbers accordingly. Hope this helps somewhat, good luck to you. The feds did us all a favor yesterday - and hopefully by the time you get the process started it will make somewhat of a difference.
If you are seriously considering the refi you might want to wait until it trickles down - check with your mortgage broker to see when the best time will be!