Please edit your OP to indicate if you are or are not wanting West coast hikes. Since you mentioned JMT I'll assume you are looking for West coast hikes (and planning on hitting up east coast hikes while at Dartmouth). With 20-25 days you are looking at very long trails. That's how long I might plan to do the JMT, but I am pretty slow.
If the JMT is the length you are looking for, there is the Big SEKI Loop which was designed to be an alternative to the JMT. It is supposed to hit the highlights of the JMT, be a loop (so easier to get transportation), and avoid the heaviest traffic of the JMT. The Superior Hiking Trail is another option and much less crowded. 310 miles through northern Minnesota.
For longer hikes you are looking at the one of the big three. Of the big three hikes in the US (east to west: Appalachian Trail, Continental Divide Trail, Pacific Crest Trail), the Continental divide trail is the least busy and hardest to coordinate (supply points).
If you are comfortable in desert environment and really good with route finding, you can attampt the not quite completed Condor Trail. In a similar vain (and starting in nearby) is the not quite official Hot Springs Trail: https://www.ariazoner.com/hot-springs-trail
Not sure if this applies to you, but a word of caution: the United States is much bigger than many Europeans realize. These trails are not easy to get to and very spread out across the country. Driving across the US takes a week. Very few trail heads have any sort of public transit options.