For resistance exercise: You don't need to pump iron in a gym to do resistance exercise. Of course, if you want to go to the gym, I wouldn't discourage you. But if you prefer to do it at home, you can. I recommend exercise tubing if you're looking for a simple but effective way to do resistance exercise at home. Exercise tubing is inexpensive and versatile (you can do lots of very different exercises with them) and they are a great way to get started with resistance exercise. You can start with a set of four for about $20. They come in colors to denote the tension. If you order them, make sure to order the strap that allows you to attach the tube to a door, and if you want to work your legs, ask for leg straps. Here are some vendors that sell them:
Usually associated with the county, senior centers offer a wide variety of services and support, along with social events. Visit your senior center or look for their website online to get more information on what they have to offer. Most sites will provide a list of programs and upcoming events that are open to the public. Getting involved in some social activities will open the doors to meeting others in your community!