Since you are targeting a specific type of clientele I would advertise in magazines and stores where they primarily sell outdoor products (REI, DICK’S, etc.) Actually REI offer their own classes on outdoor activities and physical training for those who are interested in such activities (backpacking, rock climbing, canoeing, etc.). You could partner up with them and see if you can work out some king of a deal or even promote your gym and your services to at their locations and customers.
Another idea for you would be to create a specific program that targets climbers and people who would like to use climbing as part of their cross-training regimen. Climbing can be an excellent way of working muscle groups that other conventional/traditional exercises and equipment won’t. I can think of numerous ways as how you can incorporate climbing into your training programs. Since you have the opportunity of being the head trainer there you should also have the freedom to create some great workouts. I hope this helps.