I'll second the Smoky Mountains. It is surprisingly secluded even though its the most visited National Park. Lots of ups and downs but the scenery is awesome. My favorite trail is Forney Creek. Lots to do around the park also if you only want to hike/camp for a couple of days.
Time of year? How rugged? How many miles / day? Elevation issues?
I've never been that hard-core, but it's hard to beat glaciers and waterfalls for scenery IMO. The Olympic mountains are definitely worth the trip. I also enjoyed hiking in the 14k range out in Colorado, but the miles added up fast there (5-10 every other day to move the camp plus 5-15 daily for each summit.)
It just depends on how far out you want to go and how experienced your are. If you have not done much work at elevation, I would suggest either expanding your group or doing some extra prep before spending much time above 8-10k elevations (I would think altitude sickness would put a major damper on the honeymoon spirit.)
If you're camping and scenery are more the goal than hiking itself, I've done a couple of multi-day rafting (out west) and canoe/kayak trips (as close as northern Michigan) that were both relaxing and gorgeous.
SInce it is a Honeymoon...... Jackson Hole/ Grand Teton / Yellowstone. Use Jackson as your 1st base and do some day trips to nearby Grand Tetons. Lots of nice places to stay in Jackson. Pull up stakes and go through Grand Teton to Yellowstone Park and spend a few nights on the trail, but at least one night in the Yelowstone Lodge. Leave your last night to stay in Jackson Hole again and get cleaned up and civilized.
Congrtrulations and have a great wedding!
Canyonlands National Park, Utah. Unbelievably epic scenery, relatively easy hiking/low elevation, undeniable seclusion, ancient artifacts. Truly one of the most amazing places I've ever seen, and that includes Denali, the Yukon River, the Smokies, Sedona, The Grand Canyon, giant redwoods, Yosemite, Yellowstone, the Everglades, Niagra Falls, both oceans, and the Rockies.... you get the idea.
HB
Take Amtrack out to Glacier National Park in Montana. The train takes about 36 hours, but is relaxing and they have a restaurant car, sleeper cars and an observation car with a bar downstairs. The train stops at the Park's main inn and then shuttles can take you to the trailheads. Gotta get reservations for the campsites, but it's absolutely beautiful out there. Went last year and really enjoyed it. If you go, just make sure you are both in good physical shape. It can get pretty rugged, but well worth the effort.
Can I just mention that you are going to need somewhere near a SPA and a nice hot tub. A nice day or so in the wilds on a Honeymoon might work well. Maybe your girl is a little more hard core than most.
My bride would have had some problems with a week or weekend in the wild on a honeymoon. She would have most likely been ok with 24 hours.
She would be much happier with room service, drinks at poolside and diners at a good restaurant. She would have been less happy with outdoor toilets, Water from a stream, and MRE's at fireside.
Maybe a trip to the Brice canyon and then on to VEGAS from there.