Eons ago, it seems, (40 years or so as it was my first Superliner ride and they were brand new!) I had a long layover in Omaha for the eastbound California Zephyr that I missed in Denver and flew to Omaha to 'catch' it.
I was a heavy drinker back then and told the cab driver I'd buy if he'd pour me off at the train station about 2AM. He poured me off exactly as planned. As a recovering alcoholic, I strongly don't recommend drinking your way through your layover, but spending time elsewhere is a good choice to make the time go fast.
Plan B: have a portable DVD player and watch that at the station. They may have wifi, too. Watching videos on a tiny cell phone screen 'burning up' your gigabytes data allocation is not an option I would consider. Special note: If Greensboro has any of the newer, extremely-uncomfortable seats like Amtrak has at PGH and WAS (black vinyl with 1/4" padding seat & back, brushed aluminum arm rests between each seat), DEFINITELY find some establishment that's open to spend the time.