The North Cascades are arguably the best set of mountains in the lower 48 as they are the only range offering everything in the mountaineering spectrum including long approaches, both good and bad rock climbing, ice climbing, large glaciers, steep snow, remoteness, and all types of weather. No other place in the lower 48 except perhaps the Wind River Range in Wyoming even comes close to offering this much variety. This likely plays a role as to why many of the best American alpinists come from the state of Washington. For the sake of this page, I am considering both the North Cascades National Park, and the surrounding peaks in the Washington Pass area, Mount Baker Wilderness, and Ross Lake NRA as the "North Cascades". Technically these mountains extend into southern BC but any trips done there (Slesse as an example) will be listed under the British Columbia pages.
North Cascades National Park is divided into two separate halves, with Highway 20 (North Cascades Highway) dividing them. This is one of the most scenic roads in WA and passes below many towering, steep peaks including more famous ones like Jack Mountain and Liberty Bell. The northern section of the park includes most of Mount Shuksan, the Chilliwack and Skagit ranges near the Canadian border, the entire Picket Range (most remote area in the lower 48), and Bacon Peak, which is an outlier peak in the SW corner of the northern unit. Along Highway 20 and Ross Lake (boat shuttle offered), there are a few good trailheads where you can hike into the mountains such as the Thornton Lakes, Little and Big Beaver, Goodell Creek and others that take hikers and climbers into the northern unit.
The southern unit of the park is the more visited section due to the slightly easier access (more trailheads and road access), and the better quality of climbing found in general. Highway 20, although technically enters forest service land just past the Panther Creek Bridge, closely parallels the eastern park boundary as it ascends Granite Creek prior to reaching Rainy Pass. This provides good access from the east, while the Cascade River Road provides access from the west. Most of the highest peaks within the park boundaries are in the southern unit, such as Mount Goode, Mount Buckner, Boston Peak and anything else you normally access from the Cascade River Road. Although barely within the park boundary, the Cascade Pass trail is the most popular hike in the park and is a launching point for many routes and peaks. Other well known peaks found in the southern unit are the Inspiration Group, Snowfield Peak, Mount Logan, and Ragged Ridge. Many long trails allow good access through the sweeping valleys separating these mighty peaks. In particular, the Thunder Creek/Fisher Creek Trail system is like a highway for foot traffic stretching dozens of miles taking you deep into the heart of the North Cascades. This trail launches from the Thunder Creek Campground. The Fisher Creek Trail eventually crosses Easy Pass and meets back up with Highway 20 well off to the east. From Rainy Pass, the Bridge Creek Trail heads west giving access across the southernmost reaches of the park. This area is one of my favorite places in the world I've been to, and the banner photo on my homepage (also shown below) shows a sunset on Forbidden Peak from a camp high on the Inspiration Glacier at the Base of Klawatti Peak, which is the only true nunatak in the lower 48!
The area around Washington Pass and Rainy Pass is not within the park, but is still considered North Cascades. The Liberty Bell group, Tower Mountain, Mount Hardy, Mount Silverstar, and Kangaroo Ridge areas fall into this category. These peaks actually have some of the best alpine rock climbing in the state and act as a transition zone between the wetter Cascade crest, and the drier peaks in the Pasayten, and Chelan Sawtooth Wilderness areas off to the east. The Mount Baker Wilderness is a large area just west of Mount Shuksan, and includes Mount Baker, the Twin Sisters Range, and the peaks along the Canadian border north of Baker which include the Border Peaks, Larabee and Tomyhoi, among others. This area is very frequently visited by locals from Bellingham.