Wrexham (Welsh: Wrecsam) is a city in Wales, near the English border.
Generally speaking, hitchhiking out of Wrexham tends to take time ( Roaming Pencil estimates it to have one of the longest waiting times she has encountered in Wales). On the positive side, it's possible to walk out of town in any direction.
Hitch from the A483 roundabout near the university; best to start with a Chester sign. Then you can pass Chester, get dropped off before Chester, or do whatever you want.
South towards Herefordshire, Cardiff, South Wales
Walk to the A483/A5152 junction. There's room to pull over just after the roundabout.
Other useful info
Wrexham is ~15 miles / 25km away from Chester (in England), which is often better known (especially by people who aren't from Wales). Therefore, if you're trying to reach Wrexham, it's better to focus on Chester and then make your way to Wrexham (easily hitchable via A483).