NW Raleigh camping for December

None.

If you want to search nearby use the map feature at Allstays.com
NC Campgrounds

Doubt you are going to find anything closer. Just being able to find any camping in a good size city is uncommon to begin with. I've stayed at the fairgrounds before and think that would be a good option. 9 miles and 4 miles should be pretty easy drive except for a short window during rush hour.

I think one o. f the campgrounds at Falls Lake stays open all year.
Falls Lake

Please don't think this wrong, but your seem to think a 4 mile drive and a 9 mile drive is excessive. Finding any campground closer to someone I want to visit would be hard. Sounds like you have lucked out! I have had to stay 30 miles plus away many times!

Please tell me why anybody that doesn't have to be in Raleigh in December and January would want to come here from Texas.. Forgive me if health or family business dictates same. If it's health choose Duke University Hospital. They are awesome. Even the food is good unless you are on a liquid diet.
The fairground is your best choice of the 2, but you must vacate and then return. Maybe bounce back and forth with Falls Lake but you may be dry camping at Falls that time of year.

wife and i stayed at falls lake state park last december for a long weekend. nice large sites available and no problem with water and electric but weather was mild. not a bad drive into raleigh. i have friends from richmond va that periodically stay at state fair campground. they like it, full hookups, no reservations taken i believe.