I've only experienced staying in Carmarthen once myself, so I can only go by Trip Advisor and Booking.com myself, though I can tell you to avoid the Old Priory Guest House. That's where I stayed and it was awful!
Here are some links that might help:
Spilman Hotel - has a range of double and twin rooms, including "cosy double for one"
Ivy Bush Royal Hotel - 70 ensuite rooms and parking for guests
Rose and Crown Hotel - a pub with accommodation, but rooms are recently refurbished and Booking.com gives it a rating of 8.4, might suit some
New Park Hotel is also quite central, so short walk from station, but doesn't have parking