Yoga and Pilates are your friends. They are wicked. I did often find though that I couldn't climb as hard the day after a core focussed Pilates class I guess because my abs were still hurting. This isn't a problem if you see climbing indoors as training though
Work the push movements to protect from imbalances
A bit of fingerbording
Stretching, massaging and rolling out my muscles and/or yoga/pilates
And a bit of cardio, (it has just come to me but, I wonder if bag workouts would be a good way to improve arm endurance)
In reply to candy_girl: if you want to lose weight then firstly, some sort of HIIT such as sprints, burpees, or kettlebells are more effective than steady cardio like running and many forms are less high impact (obviously sprinting is still high impact but bike sprints wouldn't be) so less chance of niggling injuries. Secondly, weight loss is 70% diet anyway.
As for other things you can do, kettlebell circuits, yoga as other have said or even hangboarding if you feel your fingers can handle it are all good options.
In reply to candy_girl: If you go 3 times a week, wouldn't a long term pass (monthly or whatever) be better value? That means you're free to do more frequent, shorter & more intense sessions, which are better if you want to get stronger, rather than stop all night just to get full value for the entrance fee.