PTI or GSO Airport is exactly 11 minutes from the main city and also 11 minutes from the Proximity Hotel. Getting an uber should not be a problem and it's a lovely small airport that operates mainly like a private airport.
The Proximity Hotel is a boutique Greensboro Treasure. Nestled perfectly within Friendly Shopping Center, it offers a variety for all to enjoy including a pool, a fitness center, bikes that can be rented to explore the area, and a European Flair restaurant called Print Works.