I always say, don't build a brand new baby website for your existing brand unless you're absolutely sure it's necessary - you're going to have to work hard to get it even just to the same level as your existing website, let alone beyond it. Plus, why cut your link profile in half? I'd definitely say build a page or section on the new location. Some things you can do to help SEs figure out you're in 2 locations:
- Make sure both locations are in Google Places or other local services. I highly recommend Universal Business Listing for this - one submission to UBL will put your business info everywhere it should be to send strong local signals. Well worth the low price.
- Mark up the addresses of each location on your site with hcard microformat - this says to search engines "here is an address." here's a wiki with everything you could possibly need on hcard microformat: http://microformats.org/wiki/hcard
- Upload a KML sitemap with your locations to Google Webmaster Tools. Here's a good guide on how to do that: http://www.martijnbeijk.com/tutorial/using-kml-for-local-seo/
- Use your city name in the title tags of pages that are about that specific location.
Best part about those last 3 suggestions - you can do them all for free.
Good luck!