I've ridden both coasts, though neither one all the way. I'd agree that the southern part of the East Coast is not all that exciting and can be very humid and hot. I did it in May - June and it was plenty hot and humid then. In fact, of all the tours I've done, the southern East Coast was one that I wouldn't particularly recommend. The northern part of the East Coast was very nice and is one I would recommend.
I did the East Coast in two parts. One was
Charleston to Lambertville, NJ. Two was from the
Pocono Mountains, PA up to Acadia NP and then down to Boston. I did this ride during the fall and was able to watch the fall colors change.
I've ridden the
Washington Coast, some of the Oregon and most of
California coast and I would agree that it is a much more interesting and pretty tour.
My advice would be to do as much of the West Coast as you can (no reason to go south of San Luis Obispo, in my view, except for transportation). Though, keep in mind that the entire West Coast might take longer than 4-6 weeks without lots of long days.
Another thought is to do what mev suggested and ride the northern part of the East Coast. If you do this, be sure to spend time in Vermont and Acadia NP.
Either of those 2 are great rides. It would be hard to go wrong with either one.