The exercise balls work great. I am a PT and used to use them for all kinds of patients with balance issues - back when I didn't know I'd be one of them. They are pretty big though, so if you have limited space it might be a problem - unless you get one that compliments your decor. I just stick mine in the closet when i'm not using it. I got mine at Target. They are available all over now - sporting goods stores, Sam's club. If you have a PT get you one, it will probably cost you 10x as much (kinda like the government spending $500 for a pencil). Mine came with a little hand pump, so if necessary, I can deflate it and it's much easier to put away.
Static, you're right about the dogs! Mine thinks she's died and gone to doggie heaven when she sees it. Fortunately, it's too big for her to get her mouth around! I usually put her out in the yard when i use it or she thinks it's playtime. Wait, she's a golden retriever - she always thinks it's playtime.
Good suggestion to make sure you have something soft to land on - just in case!