I have been quilting for about 18 months and I started by setting up space in a spare bedroom. I recently moved my sewing machine etc to the end of the family room. I put it there because it has a large window and I spend quite a bit of time there so I wanted to enjoy the sunlight. I can eventually see my quilting stuff overtaking the room but for now it is fine. I can turn on the TV while I sew and my daughter can also come and watch TV if she likes.
I'd say that the family room is a good choice but you have to do what works for you and your family. Good luck.