Haven't had a chance to vette this yet... but thought I'd put in out there... Hopefully hasn't been put on thread yet.
http://www.wisebread.com/10-most-breathtaking-day-hikes-in-the-us
This is an excellent article with some great hikes. Ones that I've had some experience on:
For the Yosemite Hike, would recommend hiking up the Mist Trail and back down the John Muir Trail. Or, better yet, carry a tent and spend the night overlooking Little Yosemite Valley. I did it that way the first time. The second time, my wife started along Tioga Road and went over the top of Clouds Rest to get to the same overlook. Came down John Muir. Both times, I couldn't muster the courage to do the cables on the back side of Half Dome.
Bright Angel. Do NOT try to go all the way to the river and back as a day hike. We reserved a campsite at the bottom and then spent two nights down there. Or try to get into Phantom Ranch, reservations are by lottery a year in advance. Even as campers, you can join the Phantom Ranch people for meals. There is also a campground halfway to the river (4.5 miles from the top), people who had camped near us reserved a night there do they didn't have to make the 9 mile hike out all in one day (4500' elevation gain from river to rim). I am in only average shape and we made it out in about 7.5-8 hours.
Glacier Highline Trail. Had total strangers come up to us in the Many Glacier campground looking for a shared car shuttle. They seemed safe enough, so we went with them up to Logan Pass, hiked the Highline, over Swiftcurrent Pass, and back down to the campground. Was something like 12-15 miles of hiking. This is one of my top 5 favorite hikes, maybe #1 in the United States (Canadian Rockies has several of my top 5).
Arches. Was there in late June...hot, hot, and more hot. We didn't do much hiking. Have taken 3 trips to Canyonlands south of Moab at other times of the year and loved it there. One trip was a 3 mile backpack the first day, set up camp in Chesler Park and did day hikes from there for a couple of full days before hiking back out. On a separate trip, we did a 3 day rafting trip and camped along the shore. Day 2 was filled with 20+ Class III-V rapids.
Denali. "Make sure you stay alert for wildlife as there have been bear encounters in the park". Understatement...we did ranger-led hikes to take advantage of a larger group, and still had to circle around a momma and two cubs.
Acadia. We cobbled together several trails and summited six different peaks. Would recommend staying on the the quieter back side away from Bar Harbor. Renting bikes and doing a circle of the carriage roads is another outstanding way to get away from the crowds.
Zion. Did Zion more as a drive through and then paid an outfitter to take our family canyoneering outside the park. The kids were only 9 or 10 and we didn't feel comfortable trying it on our own.
Trying to put together a summer trip right now. Looking like top 2 choices are Colorado, not too far west of Denver so we can drive it in day from Eastern Iowa. Or, New England...we have Massachusetts and Rhode Island to check off...thinking a day in each of those and then head up to the White Mountains in New Hampshire. They have huts along the Appalachian Trail spaced about 5 or 6 miles apart. Meals and a bunk provided. Basically, you can string several days of day hikes together and never have to sleep outside or cook your own meals. The only downside is that the huts hold up to 90 people and it is bunkrooms, so bring your earplugs.