There are lots of hostels geared for seniors in Europe, they're often called "elder hostels". I think the age minimum is 60, but could be younger. There are also family oriented hostels, especially in Scandinavia and Germany. Sometimes, there is a higher rate for guests that don't fit the "youth" window, which is sometimes only 26, but even then, it's a better deal than most hotels. We are in our thirties and usually have to pay a higher rate, but you can use your senior card to try to get a discount. Seniors discounts in Europe are often really advantageous - especially on the trains and public transit. Be sure to bring your card and be ready to show your passport to prove your age.
If you want to stay at inexpensive motels along the way, the Etap and Formule 1 chains offer pretty basic accommodations for, usually, less than 30 Euros a night. We are a family of 6, so this actually can be cheaper for us than paying individual beds in a hostel, and it's sometimes nice to have a private space!
Enjoy your travels!