North Carolina hosts the highest peak east of the Mississippi River at Mt. Mitchell (6684 ft). The easiest, and fastest, way to get to the summit is to wait until a nice spring or summer day and simply drive to the top. There's a large parking lot, visitors center, and gift shop where you can pick up a shirt to prove your summit experience. A short 0.3 mile paved path leads from the parking lot to the lookout platform where on nice days you'll experience a wide panorama of the Smoky Mountains. If you're more adventurous, the park offers several hiking trails from 0.5mi one-way to over 6mi one way at varying levels of intensity.
Be sure to wear warm clothes as the average temperature on Mt. Mitchell is 36F. It also rains often, so bring an umbrella.
Here's a great resource for current weather, maps, and general information on Mt. Mitchell (North Carolina State Parks: Mt. Michell):
https://www.ncparks.gov/mount-mitchell-state-park/home
Interesting Facts
If you look closely at the plaque on Mitchell's tomb (near the base of the observation deck), you'll see that the engraver missed the letter "I" on line 7 in "University." Oops!
Gear recommendations:
No specific recommendations other than warm clothes (layers), an umbrella if rain is in the forecast, comfortable walking shoes (summer) or boots (winter) and your wallet to pick up some Mt. Mitchell swag at the visitor's center.