I have tried to do some CURSORY reviews of the Washington laws, and found the following that might be of interest:
1) Chapter 19.142 RCW HEALTH STUDIO SERVICES
a) RCW 19.142.010 Definitions.
Unless the context clearly requires otherwise, the definitions in this section apply throughout this chapter:
(3) "Health studio" includes any person or entity engaged in the sale of instruction, training, assistance or use of facilities which purport to assist patrons to improve their physical condition or appearance through physical exercise, body building, weight loss, figure development, the martial arts, or any other similar activity.
b) RCW 19.142.030 Written contract required.
A contract for the sale of health studio services shall be in writing. A copy of the contract, as well as the rules of the health studio if not stated in the contract, shall be given to the buyer when the buyer signs the contract.
c) RCW 19.142.050 Notice of cancellation -- Refund.
After receipt of a written notice of cancellation, the health studio shall provide a refund to the buyer
within thirty days. The health studio may require the buyer to return any membership card or other materials which evidence membership in the health studio. The buyer is entitled to a refund and relief from future obligations for payments of initiation or membership fees and use fees or dues as follows:
(1) The buyer is entitled to a refund of the unused portion of any prepaid use fees or dues and relief from future obligations to pay use fees or dues concerning use after the date of cancellation.
d) RCW 19.142.100 Violations -- Application of consumer protection act.
A violation of this chapter constitutes an unfair or deceptive act or practice and is a per se violation of
the consumer protection act, chapter 19.86 RCW.
Opinion: If the tanning studio meets the definition of a 'health studio' (and I think they do by 1a above), then they must comply with a refund of your unused fees
My suggestion:
Send another letter (certified RRR). Include references to the above Codes and again ask for a refund. Ask them to provide citation to the '10 mile' statute. If they refuse, then you will need to take further action; either in the courts or through more public means (consumer reporter for media, local BBB, etc.).