Cathey's in Tucson isn't a LQS - but it's a GREAT place to buy sewing machines & sergers and take lessons. I've praised them to the heavens before. Don & Janice Cathey bring in nationally known teachers several times a year to do 'Sit and Sews.' Their staff do MANY classes each week year-round - re sewing & embroidery machines; sewing, embroidery, & serger projects; sewing machine software; probably some things I've left out. If it has to do with sewing, they'll teach you.
In Tucson, Bella is a great LQS. Lots of delicious fabric and classes. I've used their classroom to baste quilt sandwiches. They have an annual birthday sale of everything in the store on the store's birthday in February.
Thimbles in Woodbury, CT is another wonderful LQS AND Pfaff dealer. I live about 40 minutes away, so Donna often solves machine problems over the phone - the ones that are user-error or user-memory problems. She goes to Pfaff convention every year, and he learned how to do machine upkeep and repairs on Pfaffs (and other brands) for customers. She teaches lots of classes, too.