I checked online at Enterprise, just as one example.
You can rent a car at RDU and drop it off at Fayetteville Regional Airport.
For the sample data I put in (one day only--Dec 22, Noon-5:00 p.m), it looks like you can rent an economy car for a base rate of $14.42. They add a drop charge of $30. If you are in your early 20's, they add a $10.00 young renter fee. There are some other fees that bring the grand total to $68.96. It looks like there is unlimited mileage on this offer. That's good; sometimes, they charge per mile when your drop-off if different from pickup.
Also, check any discounts you might have--AAA, military etc. If you book a car online, you may need to book through the site on which you have the discount to get the discount code. Also, definitely check out Hotwire.com. Substantial discounts can be found there. Just be sure to read the fine print. Lots of disclaimers.