the area where you are staying is called San Luis Pass. That is the name of the pass from the beach to the bay.
now read this part carefully:
It is very dangerous. People drown there every year. In fact, someone drowned there just last Sunday. The currents and sandbars are numerous and change daily. The rip currents and undertow in that area are very very bad.
I've never ridden in that area, but I have seen some very nice rideable surf in the center of the pass. Head offshore about 3-400 yards, but do not ride alone - and have a tow strap and loops on your boat.
If I was you, I would get in the car and head southwest on 87 to Access Road 6 (it's a cut through the dunes about 2 miles south of where you are staying) and ride in that area.
You can go over to Galveston Island (across the long bridge over the pass), but most of the beach over there is blocked from driving.
I believe the better surf is down towards the jetty - but I'm not real sure about that. If all else fails (or it's waaay to windy in the gulf) - go back towards the actual town of Surfside and ride in the ICW (Intercoastal Waterway) and chase boat wakes. You will also find some good rollers between the jetties, but I'm not sure where you would launch to get there easily.