Indoor rock climbing! Many cities have rock climbing gyms that offer top-rope or autobelay climbing that prevents you from falling if you slip off a hold. I cli

Indoor rock climbing! Many cities have rock climbing gyms that offer top-rope or autobelay climbing that prevents you from falling if you slip off a hold. I climb actively and while I've never had a fear of heights, several of the people I climb with had a terrible fear of heights when they started climbing. In fact, after a few climbs the (now slightly diminished) fear of heights can often be what keeps climbers coming back. Indoor bouldering is also a great way to get started. I'd avoid anything outdoors as a beginner, also lead climbing is probably not your best bet.