The majority of the nearby coffee shops are in Surf City and Sneads Ferry, which is also where most, but not all, of the restaurants are as well. If you want to be able to walk to restaurants and such, I'd suggest staying right in town either in Surf City or in Topsail Beach. If you don't mind a very short car ride, you could stay anywhere at all on the island.
Island Drive is also known as Hwy 210 in North Topsail Beach and has many very nice vacation homes. It's located so that you are within about a 10 minute drive, give or take 5 minutes depending on where your home is, to either Surf City or Sneads Ferry.
As far as the other area, is it North New River Drive or is it New River Inlet Road?
The difference is that North New River Drive is the continuation of Island Drive (Hwy 210) in Surf City. Tthe road name changes when it crosses the town line.
New River Inlet Road turns off Hwy 210 near the highrise bridge in North Topsail Beach and extends to the northernmost end of the island. The vacation homes along that road are also very nice but it is a more out-of-the-way area with few restaurants, one small store and a fishing pier. It takes roughly about 10 minutes to get to Sneads Ferry from there and 15 to get to Surf City.
If you have any other questions please be sure to ask.
Edited: 9:30 am, March 05, 2013