The route we take from New Hope to Brooklyn goes through Ringoes, Neshanic Station, Raritan/Somerville, Liberty Corner, Lyons, Basking Ridge, the Great Swamp, Gillette and Kenilworth. That's where you pick up the serious traffic. From there, we go through a nicer part of Elizabeth and past Keane College. We cross U.S. 1&9 and ride through the Port of Elizabeth & Newark, something you cannot do with safety during the week. After Doremus Ave. we cross the U.S. 1&( bridges over the Passaic and Hackensack Rivers. We now arrange for volunteer driver who ******* groups over this hairy stretch from behind. Improvements have been made to the walkways (there is a thread about this in this subforum), so you might not have to ride the road. Once in Jersey City, we make our way to Hoboken and catch the ferry from the 14th St. dock to Midtown and then ride down the Hudson bike path to Warren, where we head east to the Brooklyn Bridge.
There are some public transit options later in the route. You can catch NJT trains from Somerville, Lyons, and Gillette. The route also passes close to the Elizabeth station on the Northeast Corridor, the Union Station on the Raritan Valley Line, PATH's Grove St. Station in Jersey City and PATH in Hoboken.
Some people ride all the way from Philly. The Philly to New Hope section is relatively short. If you get stuck, you can wing it or try to find a bus or train.
I take several multi-day tours every year. (On Friday I will be driving to Ohio and riding home to Philly starting Saturday, and I spent 9 days touring in the mountains of Montana back in June.) If your bike is in good mechanical shape when you start out, and you can make basic repairs, the chances of something unfixable happening are slim unless you get into a bad accident. My first tour was nearly four months. There were 13 of us for the first 3 months and then I rode home solo. Over 44,000 bike miles. Not one person had to get a ride due to a mechanical problem.