The largest multi-storey car park is at The Quadrant (on Wellington Street, SA1 3QR). It costs £4 to park here for 3 hours (parking is free on Sundays). If you bring your parking ticket to the theatre, it can be validated by one of their front of house team members and you will receive the first hour free. It's a 7-10 minute walk to the theatre from this car park at buggy pace.
There is also an open air pay and display car park on Singleton Street at the front of the theatre, which has limited spaces. Please allow plenty of time in case you need to park elsewhere. You can see all the parking options near to the Swansea Grand Theatre on the Parkopedia website.