I second the recommendation on Charisma and a few other board members who's name (apologies to them all!) I can't remember. I believe there is a section on the board for LAQ and then you can look at that user and look at their posts. See if what they do is what you are looking for. Most of the time they post pictures of work they've completed for customers.
If you are limiting yourself to a local person - check around your LQS - a lot of times the sample quilts they have hanging are done by someone who is willing to do professional work. Take a look at the samples and ask the LQS if it's possible to see the back as well as the front.
Once you find someone, get the agreement in writing. Price, what is included in the price, the type of quilting expected, any special considerations (ie a pieced back to be centered), type of batting and thread to be used, time frame, etc. Doesn't hurt to get recommendations either.
I used a LAQ once. I found her work in my LQS and I liked it and the LQS lady had her business card handy. Both of my regular LQS have a space where LAQ's can put their business cards. My lady was local, very easy to work with - of course I handed her the quilt top and told her what I wanted, she suggested something different that sounded better so I gave her the go ahead. She did an awesome job.