One of your first stops should be Oriel y Parc. Here, you'll be able to orient yourself and get some great ideas before you set out exploring.
This tourist information center is situated in Haverfordwest, a place that has lots going for it! The Blue Lagoon, St. David's Cathedral, and Whitesands Bay are other interesting sightseeing options not far away when you're done at Oriel y Parc.