I did month-long bike tours around the east coast over summers for several years, alternating between youth hostels and camping. Hostels are great; you get a kitchen, running water, shower, etc. Your on your own during the day, as they are usually closed.

It is a wonderful way to travel. It requires a certain degree of training; riding 50-100 miles a day for a month is not easy (take the weekends off), but my experience was people I met everywhere were incredibly friendly. It's also much easier to get around towns, do laundry, etc. (I think cyclists are viewed as one step up from campers. )

You do need to know how to fix and maintain your bike, which most dedicated cyclists already know how to do. And fortunately, touring requires you stay on paved roads and there are almost always other friendly cyclists around to lend a helping hand, provide a spare CO2 cartridge, etc.

But in the US, most hostels have strict age limits, which I think is a very good idea. European hostels are a little more relaxed, and that last hostel I stay in was in Ireland 5 years ago. (Had an awesome time but now I'd feel silly staying in a hostel with a bunch of kids.)