Taliesin Arts Centre sits on Swansea University's Singleton Campus, between the sweep of Singleton Park and the coast of Swansea Bay. It is a working arts venue rather than a grand monument, but its programme gives Swansea a useful cultural stop outside the city centre: theatre, film, dance, music, talks, and touring performances all pass through.
The location makes it easy to combine with a walk through the park or along the bay, and the nearby Egypt Centre adds a small but worthwhile museum angle to the visit. Check the programme before going; Taliesin is strongest when you time it for a performance, screening, or exhibition rather than treating it as a drop-in sight.