st andrews, edinburgh or strathclyde?

Depends on what course you do and how you feel about the cities themselves. Strathclyde is a good uni but St Andrews and Edinburgh are ranked significantly higher. I would personally recommend going for one of them.
Again, depends what your course is - maybe talk to other students who are taking the same courses as you if you can find a way to get in touch with them (LinkedIn, friends of friends etc.)
St Andrews is slightly better than Edinburgh just in terms of student satisfaction. Edinburgh tends to have more English and International students and St Andrews has lots of American students.
I'd say if you got offers for both Edinburgh and St Andrews, it would come down to where you want to live as both cities differ quite a bit. They are equally good unis but obviously St Andrews is so much smaller, more pub life, less nightlife and a bit quieter/wholesome. It is also small so there is less to do but if you are wanting this then it is a great choice. It is also close to Dundee and Edinburgh so you won't be stuck there. Edinburgh other hand is the capital city of Scotland so it is much bigger. The night life has a better reputation and there are lots to do such as museums, scenic walks, nice cafes etc.
Another factor you might consider is whether you want to move out. I don't know where you are currently based but say you already live in Edinburgh at get an offer from the uni, you could save money by living at home. But likewise if you definitely want to get the experience of moving out and can afford it, Glasgow or St Andrews could give you more independence.
Have you been to any open days or at the very least visited those cities? I think this would help give you feel for them. My best advice is to speak to people who have experience going to uni in these cities as they can offer you some advice.
Also depends on what course you are doing because certain unis have better (or worse) reputations based on the course. For example, medicine is probs better at Edinburgh Uni compared to St Andrews. However, Mathematics at St Andrews has a better rep than Edinburgh.
Most importantly, do what feels right for you - each of those unis listed will give you a wealth of different experiences and exposure to new environments. Either way, I'm sure you will thrive wherever you go!
Rooting for you!