The information you have been given is pretty much correct. North Carolina probably has more drag strips than any state; however, the weather here after mid-November is a roll of the dice.
Rockingham is a 1/4 mile track but they do not prep that track very well unless there is a big race. Fayetteville is a 1/4 mile but it can be a wreck at times. Dunn Benson has completely rebuilt their track and is going to run 1/4 mile, I think beginning next year. The track is closing in November and will not re-open until March. Carolina Dragway "House of Hook" would be a good choice; however, you got to look at the weather forecast.