Claire,
There are some places that specialize in vestibular rehab, but any PT has had training in it and can help you. Your doctor may have a special person or practice that they prefer, so I'd start asking there. Depending on your insurance, you may or may not need a referral from your primary care doc, but the rehab place will know if you need that or not.
I would definitely check the practice out - make sure they're licensed to do what they say they are going to do, but I don't think you need to go as into depth as you would a brain surgeon.
I would think that waiting until after the surgery would be better since you don't know for sure if you'll even have any balance issues. Mine were very minor and didn't last long, so I didn't have to go to therapy for it. I just did some exercises on my own (I'm a PT so I had a good idea what needed to be done) and I'd say I'm pretty good now with the occassional weaving when walking.
A PT should meet with you during your hospital stay and will be able to determine if you need the therapy or not, or if they think you can just work on it at home with some exercises they'll give you.
Lori