I have not hiked the AT but have the JMT. If you're still in Vegas, amazing backpacking on the JMT/PCT in the Eastern Sierras is ~5 hours away.

Some of the best hikes there which are logistically easy are: Thousand Island Lake Loop which is 2 or 3 nights starting from Red's Meadow outside Mammoth Lakes.

Also Rae Lakes Loop starting from Onion Valley Trailhead/over Kearsarge Pass (there are two ways to do Rae Lakes Loop, the one from the east approach, Onion Valley, is easier from Vegas). That's a 5-6 day hike.

Both are epic!