5-7 days... Really depends on how much vertical you wish to do a day.
Really only one or 2 places in my opinion for trails. Glacier PEAK Wilderness or Olympic National Park. Glacier Peak Wilderness will have VERY FEW folks in it generally speaking.
My #1 recommendation as there are hordes of side trips you can do and if the will is strong, many class 2,3,4,5 peaks to climb if you so wish. Glacier Peak Wilderness. Here is a 5-7 day trip. Can extend it indefinetly of course if you are a higher mileage person by adding trails(loops) north of the selected area. Chiwawa river road end. Spider Meadows. Spider Pass. Chiwawa lake/Glacier. Suiattle Pass. Cloudy pass. Image Lake(must detour to in decent weather). Buck Creek Pass. High Pass. Back to car. Yes, if you are a high mileage hiker you can do this loop in 2 days, but there are a huge number of side trails and additional loops with attractions in this area. If the weather is nice, you will want to stay forever. middle to End of July is peak time for wildflowers usually, but if heavy snow year, can be pushed back by a month. Huckleberriers are peak in Mid/late August. Beware of Black and Grizzly bears. I have seen both. Black Fly season is generally middle of July, but tends to extend only to 5000 feet leaving everything above that ok minus the other pests of course.
If higher mileage person. Then a 100 Mile trip is going Around Glacier Peak itself. Park at North Fork Sauk via city of Darrington as the other two main access points are washed out(white Chuck/Suittle river). Could do it from the Chiwawa River Road, but I would recommend skipping that portion as you have to wade Chiwawa River and road walk a ways and instead go up the Napequa River Valley to High Pass and down to Buck Creek Pass. Exceptional beauty through there along with Red Pass. DO wander up Portal Peak or over to Kololo peaks(8200 to the east of Red pass).
Glacier Peak Wilderness was not included in the North Cascades National park because at the time there was designation for keeping a National Park a wilderness and the proponents who wanted it protected did not want roads put into it. Thus, it became a Wilderness and the North Cascades National Park/Ross Lake National Recreational area became a national park. Also, the North Cascades National Park really doesn't have many trails in it to speak of or worth mentioning, as its nearly all a climbers paradise. You have a couple passes like Fisher, Cascade, Whatcom, but generally all trails that do exist in the NCNP, are in deep valleys with no views. You have to get high and go off trail to truly enjoy NCNP.
Olympic National Park. If you don't mind some off trail rambling and glacier travel do the high divide loop going from Sol Duck Hot springs and the bailey traverse over to Mt. Olympus and back to your car. The other 5 day mellow loop is situated on the Quinalt River Trailhead on the South Side.
As posted by someone else, the Pasayten Wilderness has huge number of miles of trails, but IMO isn't all that spectacular of scenery(seems exactly like Idaho). Its more something to do in the fall time for the larches or spring time because its east of the crest and less likely to be poured on. The exception is the western portion where the true crest trail runs.
PS. If you want off trail routes, I can give you TONS of them that would encompass that 5-7 days in pure bliss in good weather. Ptarmigan Traverse. Pickets Traverse. Several other traverses as well. Here is part of the Pickets. http://www.flickr.com/photos/33243403@N02/3099170058/