$150 a year sounds pretty cheap to me. Lots of reasons to work out at a gym. Some people are on a tight schedule and need to get a quick workout in over lunch, or before work, or after work. Some people like the motivation of group exercise classes, or working with a personal trainer. During winter months it is easier to work out indoors as opposed to running or cycling in the cold, or dark. Also, working out on a spinning bike has some cycling specific benefits. You can practice cadence, intervals, sprints, or hills without worrying about other bikers, dog walkers, or cars. And you can do it while blasting high energy music that would be a pretty risky thing to do out on the road. And, it will keep you in biking shape through the cold winter months if you live in the Northeast or Midwest and don't have the time or inclination to train outdoors.
Finally, a gym offers a variety of options, from weights, Yoga, kickboxing, to stationary bikes, to elliptical trainers, so you get the opportunity to cross train, all in one convenient place, where you don't have to worry about the weather, that is open 18 to 24 hours a day, every day.