I lived for 20 years in the NY metro area along the Route 1 corridor, and I will never go back. Be aware that if you do stick to Route 1, you need a high tolerance for sitting in traffic, endless lights, miles of dull freeways, predatory policing, and seemingly inescapable development. New Jersey is the most densely populated state in the country, and the other northeastern states (CT, RI, DE, MA) are not far behind.
Also be aware that the weather in summer on the East Coast is often stifling hot and humid and bug ridden, making camping miserable without A/C, even as far north as Maine. High elevation campsites are hard to find back east.
You can cross the Bay Bridge and work your way up the quieter (very relative, that quiet) coastline there. The Cape May Lewes Ferry is pricey but it will bypass Philly sprawl and take you along the Jersey Shore. Much of the Jersey Shore is heavily developed and extremely crowded in summer. You will likely be sitting in traffic for hours every weekend, even if you pay the tolls and use the Parkway. Inland just a few miles is another world, sleepy little cranberry farms, miles of sandy roads through scrubby pines in the Wharton and Byrne State Forests, a completely different environment than the rest of Jersey. If you choose not to bypass Philly...
Wilmington up to Trenton is a heavily congested traffic corridor, but if you want to head north you have to deal with it. Trenton is a ghetto and Route 1 passes right through it. Hop across the Delaware after Philly and take I-295 north to Route 1 for a quicker drive.
North of 295 Route 1 passes through endless suburban development (where I used to live) until New Brunswick NJ, where you will start wishing for low-density suburbs. I would recommend parking someplace like Monmouth Junction and taking the train into Manhattan if you want to see the sights. Traffic in New York metro area is legendary for its meanness and density, and parking is absurdly expensive in the city.
The coast of Connecticut and Rhode Island and Mass has lots of interesting places but it will also be extremely crowded in the summer. Maine's coast is beautiful but will be full of vacationers from farther south, and the prices will also be through the roof as said vacationers have lots of money.
After taking the train into New York, you can take 206 up into the scenic hill country of northwest New Jersey. You can take I-80 over to 209 and run that through the very scenic Delaware Water Gap along the PA side, but be aware that on a nice day, millions of weekenders from the city will be visiting the lakes and waterfalls and mountains of this area. You can also continue on up into Sussex County. There is no public land up there though, so camping will be a challenge.
Once you finish the Delaware Water Gap, you will have a choice: head north into the Catskill and Adirondack or Green Mountains, or take I-84 east to the New England coastline and work your way up through Boston and Portland. The mountains will become less crowded the farther north and away from the highways you go. Free camping is allowed 150 feet from roads in both parks, and in designated drive-in campsites. In the Green Mountain National Forest of southern Vermont primitive camping is allowed on many back roads. The White Mountains of northern New Hampshire are extremely scenic, and relatively cool in summer, although quite buggy. Free camping is allowed on some back roads in the White Mountain national forest. Inland Maine has plenty of camping opportunities, although the land is mostly private and owned by logging companies. Very rugged, remote and scenic country.
The places I haven't been are the New England coast between Portland and New York, and the Maine north country. I also haven't been on the Chesapeake peninsula. I can't speak for New Brunswick Canada either. The rest I'm writing from experience.
If you need anything clarified feel free to PM me.
PM if you want any more specifics.
