i'd love to try out rock climbing but unfortunately i have a fear of unstable heights :(
to be clear: indoor rock climbing
its very stable and safe, you can start easy with indoor bouldering where you're never more than 5 ft off the ground (and will by design and training fall on your back onto soft flooring if your muscles do give out)
belaying/auto belays are great for the tall stuff, you're safe cause you've either got a person or a device rated to hold your weight and more, and you'll never fall uncontrollably
the main downside you'll have to face is pretty high monthly fees, so to get good value you have to go frequently (ie more than once a week). most places also have a day fee if you just want to give it a go occasionally/for your first time.