Well for early summer / June, I would think Canyonlands, Grand Canyon, Zion, and the other national parks in the Utah / Arizona area will be too hot for long backpacking trips. I don't have any great suggestions, but wanted to support your decision to consider the amazing state of Colorado, where there is lots of excellent hiking to be had. I live in Denver, so I know The Colorado Trail may be something worth looking into. If you like that idea I can give you some more specific ideas in Colorado. The entire trail takes a few months, but you could hike several sections in 2 weeks. There will be snow in the higher Rockies along the continental divide, but there are plenty of places you can avoid snow. Although it wouldn't take 14 days, I want to mention the Black Canyon of the Gunnison National Park, one of my favorite places in Colorado.