If your goal is to make your teen-aged daughter someone else's problem for a long stretch of the summer, then yes, American Youth Hostel's Teen Treks program is probably still the way to go. It's like an overnight camp on wheels, all the way down to the austere living arrangements. But if you actually want to go with her and spend some—gulp—quality time, there are a bunch of amazing bike outfitters who operate trips within the States that cater to all sorts of groups, from families, to singles, to retired couples, to honeymooners. Here's a sampling:
Ride a high-end Trek bike and explore just about any corner of the country. The company leads trips through California wine country, Bryce and Zion national parks in Utah, Yellowstone and Grand Teton, Vermont, Western North Carolina, and even organizes a 3,240-mile cross-country expedition (though it's limited to ages 16 and older), to name a few.
Founded in 1979 by a college professor in New York who had been leading his students on bike trips through Greece, Classic Adventures is still family owned and operated. In addition to its international offerings, it also organizes weeklong adventures through Vermont's Champlain Valley, Texas hill country, the Natchez Trace in Mississippi, and upstate New York.
Based in Las Vegas, Escape Adventures specializes in Western road cycling trips. You can take a five-day bike camping trip through Death Valley, spend a week inn-hopping through the Sawtooths, or spend a week exploring the San Juan Islands. In all, it operates trips in 11 states, in addition to custom tours for groups with ten or more people. An added bonus: the support vehicles are powered by vegetable oil, making your trip a tad sustainable.
The granddaddy of posh adventure tours leads 14 trips throughout the United States, on top of its famed European bike expeditions. You can ride from inn to inn in Alaska, cruise through California wine country, take a tour of Acadia National Park, or linger among the Cascades. Most are roughly a week in length.