Student halls is certainly a no, I've never heard of student halls allowing pets. As you're not keen on those anyway you can probably just rule that out altogether to start with.
So outside that probably the tricky bit is that, if you're looking to live in shared private rental you a) need to find a shared rental where the landlord is happy with both students and pets b) find a shared rental where your flatmates are also happy to live with a cat and c) that you are comfortable with said flatmates living with your flat (as if you aren't confident they won't accidentally let your indoors only cat out or similar, that could be a problem).
It's not impossible but obviously it's a real convergence of different things you need to look for, which makes it much harder and will limit your choices for both where to live and who to live with considerably.
Living by yourself will probably simplify a lot of those matters because then you can remove the entire flatmate element from the equation so it's just about finding a landlord that's happy to take a student with a pet for a studio or 1 bed flat or similar. Of course, this adds a higher financial burden so that's worth considering.
I would recommend looking at what the rental markets and cost of living in each of those areas are budget against what your expect sources of funds would be. You would most likely be entitled to the maximum maintenance loan and possibly some bursary from your uni as being over 25, your student finance will be assessed only against your own income and with where the thresholds sit I think it would be hard to not get the maximum loan if working only part-time (if at all), which is the likely scenario (since working full-time while doing a full-time degree seems unlikely!). This may help offset some of those rental/living costs.
In this scenario then your decision on which uni to go to once you receive your offers might be significantly driven by the financial element...!