We're from NC and have been visiting Big Bend at least every other year since 78; never get tired of it. For us, staying within the Park is a major part of the experience. As you might have gathered from the previous responses, this place is a huge and you can spend a lot of time driving if you don't have a plan in place for the things you'd like to see. We found the Park website to be a great tool and the link to the Park's newspaper, The Paisano to be especially helpful
https://www.nps.gov/bibe/planyourvisit/upload/V36N1-Paisano-Spring-2016-final.pdf
It may take a bit of searching but a few years back this journal had suggestions on what to see based on the number of days you planned to visit.
I'd suggest several days in the full hookup campground at Rio Grande Village. Use that as a base to explore the attractions on the eastern and central sections of the Park. If you could go just a couple of days without hookups, moving to Cottonwood on the western end for a night or two will provide an entirely different perspective.
While there, plan for at least a half day exploring the ghost town of Terlingua just a few miles outside the western entrance to the Park. End up with dinner at the Starlight Theater which has surprisingly good food. La Kiva is a local watering hole with a really neat atmosphere even for younger children and worth a stop. Its under new ownership and the place has been completely rebuilt but the restaurant wasn't yet open when we were there last October so I can't comment on the food.
Have fun and give us a trip report with pics after your visit.