I thought it was the Canadian side that had the parks, but either way it is beautiful. I never thought I would want to go to NYC except TI see the Statue of Liberty, but it was amazing. St. Patrick's Cathedral (of course, if you are from the UK you know all about cathedrals), the Empire State Building and its view...I've gone up in the daytime and at night and for me the night view was incredible. We walked across the Brooklyn Bridge, both during the daytime and at night, both were great, but I just love the lights at night. Seeing the place where Washington stood as he became our first President was very impressive. We stopped by the Library - I love the lions - and the Flatiron building and of course the Statue of Liberty. This was a month after 9/11 so the closest we could get to Lady Liberty was the Staten Island Ferry, but that first sight of her was so moving...
Yosemite is beautiful, but if you only visit 1 park, I recommend Yellowstone instead. We spent 3 days in Yosemite and I don't feel the need to go back. We've been to Yellowstone 5 times and I plan to go back. It has so much more to see. The wildlife, the geysers, the canyon and the waterfalls. There is just so much there.
Another place we've visited and I find incredibly beautiful are the National Parks in Utah...Arches, Bryce Canyon, Zion and Canyonlands (in that order for me...DH would put Zion first).
Crater Lake and the coast of Oregon, the Columbia River Gorge - I'm from NM so that much water is downright unbelievable ( just like Niagra Falls), Mt St. Helen's.
Civil War battlefields: I've been to Gettysburg, Vicksburg, Shiloh and all were great, but what had the biggest impact on me was Andersonville in Georgia.
I'm so jealous that you will have 4 or 5 months to travel. There are still so many places I would like to go...Boston and Philly for their history, Mt Rushmore, the Badlands, the Everglades, etc.
I guess I've rambled on long enough and probably didn't help you narrow down the list, but those are the place I've been that stood out. I didn't mention the Grand Canyon since you've already been there.
Enjoy your travels, wherever you go!