I did this last year with SN, and my memory is a bit fuzzy, so pardon the vagarities.
Reaching Green Mountain Falls -the directions on the Atlas are pretty clear. From downtown, take Cimarron which turns into 24 and take 24 past Manitou, Cascade, Chipita Park. If you reach Woodland Park you've gone too far. As I remember there really is only one main road through Green Mountain Falls the town, so it should be pretty clear which road to turn off 24 (its a left) and where to park. Look at the Atlas map for specifics. Then you hike up a regular town road, and the trail will become apparent when you reach the top of the hill (it might also be a dead end, but the trail is off to the left). Again, the para for 20 on the Atlas is pretty descriptive.
Other options from this area -The Atlas offers a number of options from this area. We basically hiked up to where we were tired and had a good view, and only a few hours left of daylight, so we turned around.
Notes -While this is a short drive from the Springs and a relatively easy hike (or there are options to make it so) -I would recommend taking at least a half day so you have time to wander around Green Mountain Falls, maybe stop in somewhere for a beer or lunch. This town looks like the absolutely perfect place to be!
Also, SN got really mad at me because not only did I almost get caught when Wiley pooped on an unsuspecting neighbor's lawn and by the time I found a bag the neighbor was out so I left it there, but also I had Wiley off leash. Some sort of patrol man on a golf cart saw us and told us we needed a leash, so we had to walk back down to the car and make a makeshift leash out of a string and then walk back up. So leash and control your dog around these parts, it seems.
This and the cover photo are the views from the top where we stopped. That road right there is 24.
This must be Catamount Creek Falls which we encountered right when we headed left up the trail from the town road in Green Mountain Falls. There looked to be some sort of water facility off to the left, and then to the right (but the trail bends to the right so the falls are on the left) are these falls.
Some pretty wildflowers along the trail
Wildflowers by Catamount Creek Falls
The road that we took up (town road -there were houses on it) to the trailhead
Apparently we passed Mountain Ave. I remember being unsure as we walked up this road and came down, but it seems all roads lead out so you should be ok. And basically just hike up the hill from the bottom and the trailhead should be at the top.