1.) If the vacating tenant has been a long-term tenant, and you had a good relationship, simply ask him. I bet over the years he's followed the neighborhood and knows from friends and fellow renters. He can tell you if he thinks you should charge more or less. Feedback from your vacating residents should be ONE piece of the info you assemble to determine.
2.) The quickest way to figure out the market rent is to put your tenant "shopping" hat on and start looking. I observe area rentals (signs, newspaper, etc.), see how they are priced, and watch to see how long they stay vacant. Many times, I'll even stop by to get up close to see the condition of the investment property. In every case, one that is priced right and sits for very long has "issues".
3.) Another resource is a property manager with local rentals (and a website) who knows what they're doing. They make the most money by pricing at the top of the market and usually have little interest in discounting unless a property sits vacant for too long. I usually price mine 2% to 5% below their prices.
The caveat with property managers is that some have owners that force them to overprice. That happens fairly often, but it is usually pretty obvious.