Not much to recommend in town. If you are going north from El Paso there is Oliver Lee State Park about 10 miles south of Alamogordo. East or west of town have already been covered.
Some construction on the west side of town. You can avoid it by taking Loop 375 around the east side to 54 north. If you need fuel you can get off the loop at Montana Ave and go east a half mile to the Wal Mart. They are set up for easy in and out for RVs. Get off 54 at MLK boulevard and take it north about 6 miles then go over the hill on NM 404. You will hit I 10 about 3 miles north of Camping World. There is a NM State Park (Leesburg Dam) at Radium Springs off I-25.