Here are short descriptions of cheap car free vacations I've done over the years. They fall into two categories.
1) The state park circuit. I used to pack up the tent and some stuff on the back of my ten speed and travel for several days from state park to state park in a big loop, returning home on the last day. I did this in the summer so I would only go to parks with swimming holes. My trick was to keep the distances short enough that I could stop pretty early. Then, with the load off the bike I'd some times ride into the nearest town or explore a little bit or cool down in the swimming hole. The idea here is to get out of town and visit state parks not cover miles.
Another trick was that I'd go to bed early and leave early to get as much cycling done in the cooler morning. I remember leaving parks before the ranger opened the gates. There are fewer cars on the highways in the early morning too. In the hot afternoon you are hanging out at the next park not sweating on the highway.
A semi-car free version of this is popular in DC. A van service will pick you and your bike up VERY early and take you to Cumberland MD. From there you can bike down an historic canal towpath back to DC. The National park service maintains primitive campgrounds every 5 miles or so, or you can do the B&B thing. This would be a great week long trip for a family. There are many historic sites along the way. I did it in 4 days and didn't get to take as many side trips as I wanted to. Someone from out of town could Amtrak to DC do the DC tourist stuff for a few days and pedal the canal for an outdoorsy experience.
2) The Amtrak trek. I hate the boxes amtrak usually makes you pack your bike in only for the principle of the thing. There used to be a train on the east coast called the Vermonter that let you roll your bike on. This train goes to some very bikeable locations. I heard a rumour that they stopped this service- is it true? Anyway, Philly and DC are bikeable cities to visit. DC is a huge vacation destination. The boxes aren't really that bad, you can reassemble your bike in the train station. The Amtrak employees seem sympathetic. You need to bring your own tools.
My best Amtrak trek was when I took the Vermonter to St. Albans VT in the Lake champlain region. We biked across the border to Quebec and spent a week biking around Quebec. You could probably stay in the US and bike around Vermont if you are someone with border crossing issues. We met several families on bike trips on the Vermont side of the border. You could probably camp but we did the B&B thing. Most B&Bs where we stayed had sheds for bikes and were super welcoming. One had $5 discount for bikers. The idea is to use the train to get close, then bike the rest of the way to your vacation destination. There are variations on this theme of course.
Any other cheap car-free vacation ideas?