I stayed in the Ibis Styles on St Andrew Square last June. It was awesome - very nice staff, awesome included breakfast although the rooms are small. I did not find it noisy at all. My room faced the back of the hotel. It may not be in your price range. IF you book, go thru the Accor app (hotel group). I somehow got on a travel agent site and they were charging me a "fee" of more than one night in the hotel. I was able to cancel without penalty and rebooked thru the official app.
I also stayed a couple of nights at the Parliament House Hotel which is not on Saint Andrew Square but within walking distance. I found it more noisy from a bus stop across the Main Street from the back of this hotel as well as spill over from a restaurant.
I also had recommendations for the Premier Inn York Place but decided I liked the look of ST Andrew Square better. Lots of nice restaurants around the square.