I am asked frequently how I got hold of GreenwichCT.com as everyone assumes it was registered ages ago. They are right, it was registered a long time ago right when domains were starting to be used up. I purchased the domain from someone in california that had bought it as an investment and was "sitting on it" earning money from people clicking to generic links about Greenwich CT. This domain was not inexpensive and cost a lot of money, though I feel that it was well worth it to me as it has helped to kick my brand as a Greenwich CT Realtor.
Google says that they don't place much value on the terms in your domain, though my site, which I have been working on for only a couple years, places on the first page for almost all Greenwich ct real estate search terms. Yes, I feel that this is due to a ton of hard work in posting and building up a site containing original content on my market, but I also feel that the domain itself has had a ton to do with the SEO (Search Engine Optimization) placement. I believe that paying up for a domain is a wise investment, but only if you are getting the absolute best domain name in your market. A AAA+ domain like GreenwichCT.com in a town where the town's own website is GreenwichCT.org can be a huge factor in getting your site up and running. I also own GreenwichCTRealEstate.com, which I plan on using in the coming months.
Paying up for an A- (or lower) domain domain might not help you in the search results, so I wouldn't recommend going crazy. There are plenty of good domains (your name for example) that might be available to grab or buy on a site like Sedo.com for a decent price.