Get out of the notion of hiking “a trail”, and hike where there are trails. Pick an ecosystem or a mountain range that interests you and traverse it. Lots of options out there for a month long journey.
A couple years ago with a similiar amount of time available I traversed the Greater Yellowstone Ecosystem from Big Sandy, WY to Red Lodge, MT. Hiked the length of the Winds, did a big curve through Yellowstone, and ended by crossing the Beartooths. I hiked some of the CDT but found it asthetically inferior to alternative routes in many cases (e.g. the Cirque of the towers in the Winds and the thorofare in Yellowstone). Look at the lay of the land and figure out the best way to traverse it. It makes planning much more fun and the hike more satisfying. Hike to see the land, not to complete a trail.
Of course, this strategy is especially appealing if you are a map freak like me.
Hans Berg