There is tons of legit way to exercise, and lifting weight in a gym isn't the only way. It may be worth looking at sports clubs in your town, no matter you want to practice Karate, volley ball or even rock dancing these are fun and legit way to exercise. They also tend to be more social than fitness gym which helps with motivation.
Now regarding what you can do at home, depending what you call home. A fitness mat and a rubber band can bring you far. Body weight training does work too. While not strictly at home running is fun too, and goes from beginner who alternate one minute running and one minute running to people preparing Ultra Marathon
Oh I forgot about that one