Denver - Rockies. Looks like that has been covered here. I will add stay on east coast time and starting early. I found on several occasions (starting before 6am) to meet very few people on the way up, but coming down meeting a steady stream of climbers in the other direction.
Seattle (my favorite, done 5 or 6 climbing/hiking vacations out there)) -
Tons of peaks to climb that are comparable in difficulty to the White mountain hikes -->
http://www.summitpost.org/shriner-peak-wa/154842
http://www.summitpost.org/burroughs-mountain-mount-rainier-sunrise/340516
http://www.summitpost.org/plummer-peak/151691
http://www.summitpost.org/hidden-lake-peaks/153469
http://www.summitpost.org/sourdough-mountain/152814
http://www.summitpost.org/mount-aix/152717
I did not encounter crowds on any of these peaks. I do not know if those count as "real" peaks, they could be fake, but you can view "real" peaks from them. Seattle is my favorite city to visit.
Much more glaciers to view in WA vs CO.
Also check out the books from the Mountaineers 100 Hikes series -->
http://www.mountaineersbooks.org/100-Classic-Hikes-Washington-3rd-ed-P1680.aspx
(they also have a very nice New England book)
Calgary (if Canada is not too exotic) & Canadian Rockies (2 trips in the past):
Drive the Icefields parkway as previously mentioned. It would be about a 2 hour drive (if memory serves) to Lake Louise if you drove straight there, but I can't imagine doing that. I was always stopping to look at the scenery and roadside wildlife (Elk). Much more wild feel to it then Colorado (from my experience). Mountains not as high but much more in the way of "mountaineers" mountains, mountains you can't reach the summits (safely) without technical gear. Watch the movie "The Edge" starring Anthony Hopkins, much of it was filmed in that region. Your trip may ruin that movie though, they are supposed to be lost in the Alaskan outback, and I can recognize some scenes where they are at pretty popular tourist destinations, such as Valley of the Ten Peaks.
Here is a very nice relatively easy peak I did in the lake Louise region -->
http://www.summitpost.org/mount-fairview/151994
http://www.summitpost.org/big-bee-hive/232836
On my bucket list -->
http://www.summitpost.org/mount-temple/150408
http://www.summitpost.org/mount-niblock/153381
The beehive trail had a fair amount of traffic on it, but very nice.
More info, this book is nicknamed "Suicide in Canadian Rockies" (his idea of moderate is pretty tough in my book) -->
https://www.amazon.com/Scrambles-Canadian-Rockies-Alan-Kane/dp/1771600977
You can hire a guide if it is in your budget and you do not know glacier travel or technical climbing on your own, and want to climb one of the glacier peaks. I did several glacier peaks this way. Alpine Club of Canada has several camps, the GMC I was in many years ago was very nice.