I just got a pup, and I'm trying to find some good, dog-friendly trails to hike with him! I've hiked out of the Dunraven trailhead near Drake, and that was a pretty good hike. Fairly easy with lots of water crossings.
Do you have a car? Head up the Poudre areas and there's some fun hikes up round there. Also Veedavous (sp?) up by I-80 in Wyoming is a great place to explore on weekends or hiking with a bunch of mates.
If your keen for a 2000 foot ascent, check out the grey rock hike up the poudre...best day hike in the area and you and you dog will love it. It is also doable in the winter depending on snow coverage, may not be able to summit. Also check out Lory State Park, many many hikes. Don't know their dog policies though. Also the poudre river trail is great, it actually gets plowed before the roads do. Great to go on a bike ride with dog on.