As I said before, this is a large, diverse country. I assert, and I'll guess you would agree, that you cannot see it all in your time-frame, especially on a bicycle. If you're willing to take some faster means of transportation here and there, you can expand your range. Each state has something unique to offer. It's just difficult to figure out a logical way to connect them, and impossible to cover everything.
Here's one possibility. I'm sure others would have different opinions. This will show you, in this order, the Northeast, the upper Midwest, the Northern Rockies, the West Coast, the Southwest desert, the lower Midwest, the South, and the Atlantic Coast. It's a bit too much bus travel for my tastes, but maybe this would suit you.
Follow the Northern Tier from Bar Harbor to Niagara Falls (about 10 days).
Take a bus/plane to Minneapolis (about two days).
Follow the Northern Tier again from Minneapolis to Glacier National Park (about 15 days).
Take a bus Portland OR (one day).
Follow the Pacific Coast route to San Franscisco (10 days).
Take a bus/plane to San Diego (one day).
Follow the Southern Tier route to Wickenburg, AZ (6 days).
Take the Grand Canyon Connector to the Grand Canyon and then on to Cedar City UT (9 days).
Take the Western Express route and TransAm to somewhere in Kansas (14 days).
Take a bus to Carbondale, IL (2 days).
Continue on the TransAm to Cave-In-Rock, IL (one day).
Take the Underground Railroad route to Baton Rouge, LA (10 days).
Take the Southern Tier route to St Augustine, FL (10 days).
Take the Atlantic Coast route up to Philadelphia, PA (15 days).
That's 106 days, or about 3.5 months.