When looking at a local market I want to compete in, I often look at the competition. Look for someone who is either clearly doing SEO, or has a very solid grasp on the market. Then I'll use a tool like Ahrefs, and see what keywords are currently bringing them in traffic. (They're getting rid of that tool in a few weeks, so I'll have to find another).
I've found reverse engineering the competitors holds on the market is a great strategy to either use or build off of.
And then of course, as people mentioned you can use the Google Keyword Tool. On the left column, just make sure you make it include the city name. If you're trying to go for multiple cities, you can enter all of them in separately and it will show any of the matches in the results. It doesn't help with showing you additional locations, but if you generally know the list of places; it should speed things up a decent amount.
Hope that helps. ~englandrm