My husband and I have never been to Colorado, probably because we are not skiers, campers, fisherman, or serious hikers. We do enjoy short hikes (3-4 mi) and biking paved trails.We would love to see the mountains and explore using about 7 days in either June or July. Would you recommend June over July? Would you recommend staying at ski resort? (No more that $200 a night with taxes.) Is there a central location that would give us access to many places? Any help setting up an itinerary would be greatly appreciated!

One of my favorite stops along the route of the Amtrak California Zephyr is the town of Glenwood Springs. There is a beautiful paved bike/walking route east of town along the Colorado River and I-70 through the Glenwood Canyon.
There are two big OLD hotels near the world's largest hot spring fed swimming pool. There are several newer hotels and motels in town as well. There is a gondola ride up to the Glenwood Cavern.
You can also hike up to the top of the hill to the cemetery and see the memorial stone for Doc Holliday.
There is a great bus service from Glenwood Springs up to Aspen. You can also visit Maroon Bells by bus. Late June or early July would be my choice. One time I was coming through on the train in December. I saw someone swimming in the pool while I was on the train waiting at the station.
Another stop on the CZ route is at Fraser/Winter Park which is the first stop west of Denver. That would be a great spot to visit Rocky Mt. NP

WOW! That sounds great!

July would be better than June. Early June can still be very cool, maybe snow on higher passes, and access to some hike trails could still be muddy. Generally ski area are good choice in the summer because lodging rate and restaurants can be very reasonable. Places like Breckenridge, Frisco, Vail would be good center point. There are many interesting areas within a couple of hours of Breck -- Mineral Trail in Leadville, Georgetown Loop Railroad, hot springs in Glenwood and Glenwood Canyon, etc. A little further would put you in our wine country or at Aspen and the Maroon Bells. And a bit further you could do the Trail Ridge road through the Rocky Mt Nat Park. Lots of options.

Last year we were eastbound on the CZ on May 18 east of Glenwood Springs (near Kremmling). I saw cows out in a pasture up to their knees in snow. It had all melted by the time we came back through on June 2.
You might be able to get some late season skiing at Aspen if you went in early June.

Aspen will close just like all of the other major ski resorts within a couple weeks of Easter. Easter is the psychological close of the ski season regardless of the date. The only possibility of late skiing would be Arapahoe Basin. I have skied there as late as May 25 not because I wanted to but because of an out-of-town who insisted on skiing. It was great two hours.

So in other words, you aren't looking for late season skiing in early June?

I would wait until late June or early July for all the reasons mentioned - some areas will still have snow in early June and others will still be muddy. You could/should visit a couple locations and explore. RMNP is great and has a decent number of shorter hikes that would suit you, but Estes Park is very touristy and not very relaxing. Maybe stay there a max of 2 days, then head over Trail Ridge Road to your next destination and spend the rest of your time at one of the ski towns.

Ditto for July, especially if you have hot weather at home (gives a nice relief). I like Glenwood Springs, but not for entire week. I've been able to find decent prices on condos in Breckenridge. And that may translate to other ski towns. I kind of wonder if they are overbuilding in Breck, making prices pretty reasonable. I have stayed in the heart of breck with a kitchenette and lots of space (kids) for less than the cost of a standard business type hotel on the route out there.

Breckenridge, technically speaking, probably is over built for summer activity. But they are no different than any other ski area. The major business is winter skiing. Vail has tried to overcome some of this problem with a huge number of summer programs especially summer sports programs and camps. Breckenridge has summer promotion but not to the same degree. You can always get good rates in the summer.