Vagabond,
I am afraid of heights also but I and my family zip-lined in Belize and Cave tubed and had a blast. In Belize they started out not very high and worked there way up, my wife loved it also. in Belize we used this company Butts Up!! Cave-Tubing.com - Belize Cave Tubing, Zipline, ATV Tours
Butts Up Cave Tubing - Belize City - Reviews of Butts Up Cave Tubing - TripAdvisor