Don’t you settle, never settle! And isn’t it great to experience the progression you have made to be venturing further afield 
I’m all for you venturing into the gym just because I’m addicted too 
The tread mill is an obvious must, so that goes without saying and you can set the pace as slow as you need, plus there’s 2 big arms either side of you to help maintain balance. There will also be at least 2 types of exercise bike to choose from.
I started a year ago, whilst balance was still very iffy and still right side weakness both arm and leg. Fortunately there was a lot of varied seated equipment I could use so I didn’t have to concern myself with my balance issues particularly in the beginning (I already had a separate workout to address that using a balance board).
There’s also the Steps machine, which I use a lot to try reactivating issues with drop foot.
Seated Leg press, upright seat with a large vertical plate to put your feet on and push out in front of you. There’s probably also a reclined one.
Hip Abduction (also Hip Adduction just no photo of that)
Leg Extensions
Seated Leg Curl
Naturally these are only a few and won’t look the same as at Total Fitness. But this give you an idea of the sort of things you will be able to do there.
Most newbies to the gym just spend their first few times playing around with the equipment to see what it can do for them. If this is your first time in a gym (as it was with me) you can probably arrange for a staff member to show you around and demonstrate how the various apparatus works.
So as you can see, there’s a lot for you to choose from so don’t you ever think you have to limit yourself to the tread mill and pool! 
There will also be a whole gamut of seated equipment for upper body too. I just haven’t included any as I’m not sure what you are capable of with regard to your left arm. And I won’t even start on the free weights, bars, dumbbells and other equipment they’re likely to have there which you could utilise.
I wait to post this 'til I could get a few pics during the quieter times at the gym.
Hope it raises your spirits a bit, and I’m sure your physio therapist will have good advice for you too on what would benefit you there.
Good Luck 
