Why are you thinking the gym would be no good for you???
ALL cardio equipment is ideal for people with bad balance as the equipment has a sturdy bar at the front which you can hold on to for support. As long as you have got strength in your arms, there is no problem. Just because we see people on the TV running on treadmills doesn’t mean we have to - we can take everything at our own pace.
At the gym you get to use everything - treadmill, cross trainer, exercise bike and stepper, not to mention all the resistance equipment which you have to sit down to use anyway.
My balance is completely shot and I find it difficult walking any distance, but recently at the gym on the treadmill I walked a whole mile - yippee! Obviously I felt the effects after, but that wore off quite quickly and I was so happy to have achieved my goal. There is no way I could have done it without holding on.
I’m sure if you went to your local gym and explained your lack of balance, they’d be happy to show you round & explain the equipment.