The Absarokas are perhaps the largest blob of undefined mountains in the lower 48 states as they are a large mass of volcanic peaks with no real way to easily separate them. They generally run north to south encircling the north and east sides of Yellowstone National Park, and are remnant peaks of the previous Yellowstone super-volcanic eruptions. Most of the peaks are somewhat gentle however a few areas, such as the peaks near the northeast corner of the park have very rugged faces that can only be climbed in winter due to the loose nature of the rock. In particular, Amphitheater Mountain and Pilot Peak come to mind as being difficult peaks to attain (although Pilot Peak lies within Wyoming by a mere 1.8 miles!)
In general, the northern terminus of the Absarokas is the Yellowstone River and the town of Livingston. In fact, Livingston Peak is the northernmost major peak in the entire Absarokas. Although the range continues south all the way to Togwotee Pass in Wyoming, where US Highway 26 heads east from the Tetons, this page is designated for the section of the Absaroka Range in Montana (excluding the Beartooth Mountains, which is a separate range geologically and has it's own section on my website).
As stated above, the Beartooth Range is the eastern extent of the Absarokas in Montana, specifically the Boulder River Valley and the boundary between the Gallatin and Custer National Forests, where the gentle, more volcanic nature of the mountains with few lakes transitions into the granitic and metamorphic peaks with hundreds of very large lakes. This boundary is somewhat obscure but follows the National Forest boundary quite closely.
On the western side, the Absarokas abruptly end at the Yellowstone River Valley (AKA Paradise Valley) which extends from Livingston, south to Gardner and into Yellowstone. Much of the eastern half of Yellowstone National Park consists of the Absaroka Range. To the west of Paradise Valley lies the second range described in this section; the Gallatin Range. This range, although geologically similar to the Absarokas, is distinguished due to the Yellowstone River that has since cut through the caldera rim and found its way north to the plains. Like the Absarokas, the Gallatin Range are the remains of ancient lava flows, and lies both in Montana and Wyoming. Much of the western half of Yellowstone consists of the Gallatin Mountains with Mount Holmes and Electric Peak being the highest two peaks.
The most famous areas in the Montana section of both of these ranges are Hyalite Canyon and the surrounding peaks for the Gallatin, and the Mount Cowen area for the Absarokas. Mount Cowen in Particular is especially interesting because the rock is granite, which differs from the rest of the crumbling volcanic rock found in the area, and provides endless climbing and mountaineering potential.
Access to both areas is primarily via Paradise Valley, although the east side of the Gallatin Range is littered with private Property and Hyalite Canyon is a better way to access this range. Plus, Hyalite is a very short drive from Bozeman, however the road is closed from April 1st to May 15th every year despite being plowed through the winter to provide access for ice climbers. The Mill Creek Road has great access deep into the Montana Absarokas.