It's sometimes difficult for adults to learn something new because they're used to already being good at what they do, whatever that may be. But sooner or later, they get the urge to get off their butts and do something about their fitness.
Running is popular (and cheap - unless you feel the need to get ALL the gear), but there are many reasons this may not work for you. Getting a gym membership is cheap, but again, the self discipline is harder - and if you get a personal trainer (which is very effective) you will pay upwards of $70/hr whereas karate costs about 1/10th that!
You're already too old to become a World Champion (you have to start at 8 or 9 yrs for that) and so there's no hurry to achieve your black belt. You don't have to win tournaments (though it's fun trying) - the ONLY person you NEED to be better than is yourself, but you can do that at your own pace. It's something you can continue doing into your 70s, unlike tennis, surfing, cycling, or any kind of ball sport! It's a great workout that improves your eye-hand coordination, your strength and agility, and your fitness.
Karate is a very good, all-round form of exercise that works every part of your body, unlike so many other sports where usually only certain parts of your body are emphasised. It's also something you can do by yourself OR with friends and family. The only discipline required is that you turn up to class. The rest of it is up to the instructor. There's of course the added bonus that you will acquire the basics of self-defence too. No, it's not the way to ultimate self-defence. Nothing is.
Come along and give it a try.