Gregory Canyon is a nice narrow canyon with great foliage and wildflowers in spring. It follows a small stream most of the way with some crossings and opportunities to see some water in the spring. It is only about a mile to the top but connects with trails at the top to allow for some great loop hikes. My favorite is to take a left at the top onto the Ranger Trail. This will take you to a cool old ranger cabin. At the cabin, take a left up the EM Greenman trail. The Greenman trail swithbacks upward for a while until it gets to the Saddle Rock trail. At this point, you can choose to go higher on the Greenman trail and summit Green Mountain or take the Saddle Rock trail back to where you started at the base of Gregory Canyon.
There is a small parking lot for Gregory Canyon at the Flagstaff Trailhead, just past the Chataqua area at the base of Flagstaff road. However, since it is small I would recommend parking at Chautauqua (or on Baseline road somewhere in between) and taking the lower north trail up from Chautauqua.