In a word yes, although not by much. In addition to varying by state, interest rates can also vary by the city that you live in.

In general, interest rates are based on 2 things: 1) risk and 2) what the bank is borrowing money at. So, if you have an 800 FICO and are putting 50% down but the Fed rate (the rate the fed charges banks to lend them money) is 9%, expect your rate to be above that. If the Fed rate is low, but you are a high-risk borrower, expect your rate to be significantly higher than what the bank is being charged to borrow the money. 

So what does this have to do with the interest rate depending on geography? Well, while your credit score, income, and the amount you are putting down are of the utmost importance when determining risk, where you live is also factored in. During the Real Estate bust of 07' and beyond, places like Las Vegas, Phoenix, and Miami were deflating at a much faster rate than the rest of the country. Banks naturally were more skittish to lend there, as a foreclosed home was going to lose them more money in a place like Phoenix than in New York City. Thus, the lending requirements in High Risk areas or "declining markets", as the industry deemed them, became more stringent.  Interest rate premiums were tacked on, as well.

So, if you are paying a slightly higher rate in your neck of the woods, you can blame your neighbors for not paying their mortgages on time.