Mount Monroe offers a truly picturesque hiking experience. Among the Presidential Range, I’d consider it to be on the easier side, especially if you ascend via the Ammonoosuc Ravine Trail and take a refreshing break at the Lake of the Clouds Hut.
I have hiked Mount Monroe twice, once using Edmands Path and the other time via Ammonoosuc Ravine. Edmands Path offers more parking and is less crowded. On the other hand, Ammonoosuc Ravine is a popular route for summiting Mt. Washington, so both the parking and the trails tend to be more congested. This also means that the Lake of the Clouds Hut is often crowded with the Mt. Washington hikers.
Mount Monroe is quite dog-friendly, whether you choose Edmands Path or the Ammonoosuc Ravine Trail for your ascent. Both trails are steep, but neither features bouldering or rock scrambles that a pup accustomed to hiking in the White Mountains couldn’t handle.
*Please note that dogs are not allowed inside the Lake of the Clouds Hut.