Before i nominate my favorites, i'd like to chime in AGAINST any trail to a summit that is hiked solely because it is the shortest route. For example, it wouldn't make sense to nominate the Marcy Dam route to the top of Marcy, when there are other more beautiful and memorable trails that lead there. Same would hold true for Mt. Elbert, Mt. Whitney, etc etc. I'm sure the main trails will get nominations because people have great memories of reaching the top of something, but i hope that the BEST (most unique, beautiful) trails to summits will get the nod!
My very favorites, non-technical 20 miles or less:
Vermont: Mt. Mansfield via the Maple Ridge - Sunset Ridge loop. wow.
New Hampshire: Great Gulf, Airline, and Franconia Loop would all be a tie in my book, so i won't pick.
Arizona/Utah: Paria Canyon via Buckskin Gulch, exiting Whitehouse trailhead. This is usually a segment of a longer backpack, but can be done as a long, amazing dayhike.
north of San Francisco: Matt Davis-Steep Ravine-Dipsea loop on Mt. Tamalpais. Ocean, redwoods, great wildlife, and back to the ocean as the sun sets. All uncrowded and within an hour of San Francisco. (I guess if it makes the book it won't be uncrowded anymore.)
Columbia Gorge, OR: Triple Falls trail. More waterfall for your buck within an hour drive + an hour's walk of a big city than i could imagine.
Maui: Haleakala, Sea to Summit, via Kaupo and Sliding Sands trails. Just makes the 20-mile cut off, and it's a big day. But you get the ocean, waterfall cliffs, the massive moonscape crater, and the top of the island.
Oahu: like NH, there's a whole lot that would tie for best hike. Still, i think my favorite is Ka'au Crater, where you climb up along several waterfalls to reach a crater that's hidden from viewing from any other vantage point. Problem is, it's "technically" a closed trail. Everyone hikes it though.