If staying at a Marriott is key, does it have to be a Marriott hotel, or do your free nights work at other properties in the corporation? I see that Breckenridge has a Marriott, and the ski resort there has both alpine slides and alpine coaster, although for sheer convenient location, Frisco, just up the road, has better access to I-70 and the additional towns and resort areas along it, for day trips. Silverthorne and Dillon are pretty much adjacent to Frisco. Those towns, as well as Breck, are connected by a paved trail, great for walking (and, frankly, bicycling). Lots of easy hiking in the area is available, throughout Summit County.
Much has been mentioned about Grand County locations, Granby, Grand Lake, Winter Park. We actually spend a lot more time up there - fantastic hiking, views, and lots fewer crowds than in Summit County! As far as the YMCA of the Rockies, in addition to their location in Estes Park, on the east “Front Range” side of Rocky Mountain Nat’l. Park, they also have a location on the western “Middle Park” side, just south of Granby. The YMCA Snow Mountain Ranch has lodges and large and small cabins. They also offer yurts to stay in. I believe all are furnished, but haven’t personally stayed in them, so you’d want to check all that out. There are miles and miles of trails there. One outstanding hike is the Waterfall Trail, just over a mile up to a small waterfall - just over 2 miles, round trip. Another is Ninemile Mountain - steeper, but not too long, and the trail was improved 3 years ago. The trailhead is just steps away from several of the cabins, or a very short (but steep and winding) drive from the rest of the facilities. They have a summer tubing hill, archery, olympic pool, lots of other activities. They’re also close to Winter Park resort, with Colorado’s longest alpine slide - side by side tracks, so you can race each other to the bottom, Gondola (installed 3 years ago), and hiking on the mountain. You can ride up, then hike around, and ride back down, or hike down. They’re also very close to Granby Ranch, a smaller ski area with lifts and an extensive summer hiking trails.
As noted, Granby is a short distance to Grand Lake and RMNP. A short drive west is Hot Sulphur Springs, smaller than Glenwood, but a fabulous soak, right by the Colorado River. and its spectacular Gore Canyon drive. Carol mentioned fabulous hikes in the National Forest south of RMNP - I’ll bet one of those was Monarch Lake. It’s a satisfying 4 mile hike all the way around, through forest and interesting rock formations, but you can go shorter or much longer in the area, if you want. Seeing moose is almost guaranteed - but you’ll definitely come across lots of birds and other wildlife.
The area, as with much of the Colorado mountains, now has many condos and houses being rented out - Vrbo, Airbnb, etc. - but Snow Mountain Ranch might work, if using Marriott nights isn’t required. Fraser and Tabernash (named after a prominent Ute chief) are between Winter Park and Granby - additional places to look for stays. Driving from the Front Range, if you take I-70 to the Empire exit, then drive over Berthoud Pass to the Middle Park side, there’s a trail (closed-off dirt road) right at the Berthoud Pass parking lot. It goes up Colorado Mines Peak, 1,200 feet to the top of the Continental Divide. It’s one of the best, most accessible hikes available, almost all above treeline, but not for a windy day.
Telluride, Durango, or Cortez, in the far southwest of Colorado, also have a lot of spectacular scenery and adventure opportunities. Mesa Verde National Park, with the cliff-dwellings and desert hiking options, is a site from a Native American culture 1,000 years ago.
More recent Ute, Mountain Ute, and Arapaho nations were mobile, and didn’t leave too many permanent sites that make for easy visiting now. Maybe there are opportunities you can research and discover, but that could take some work.