The nearest rail station is Leamington Spa, which is a 12 minute walk to the the Royal Spa Centre at buggy pace. Fast, regular services to Coventry and Birmingham run into the station, and there is a Chiltern Railways connection to London, and Virgin Cross-Country service.
If you're travelling by bus, the National Express bus services stop close by to the theatre (within 5 minutes walk at buggy pace) on Hamilton Terrace.
Lots of local bus services stop at the War Memorial on the Parade, which is a 5 minute walk to the theatre.
Visit Google Maps to plan your journey by public transport: https://goo.gl/maps/Ngt9tgiTYAJnsZ667