If you're looking for cheap housing, staying at a hostel is the way to go. While they are not a first class hotel, they are affordable because of that reason. Sleeping accommodations often include bunk beds in a dormitory sleeping four to 20 people. If you're a light sleeper, request a room with only a few people so the snoring won't keep you awake. Many hostels today offer an included breakfast and access to the kitchen for other meals. Washing machines and dryers are often available, sometimes for free. If you want to wash a few clothes in the sink, bring a drain plug as most sinks don't have one. There are over 3,000 hostels in Europe, with prices ranging from €9-€100 ($11-$123)(most are €20-€30 ($25-$37)) per night. If you're just in Europe to visit and sight-see, you want to spend much time at the hotel/hostel anyway, so why not opt for cheaper housing, and spend your money on something worthwhile?

This site has a list of and information on private hostels across Europe. While private hostels don't necessarily conform to the same standards as those in a chain, most today are respectable. What's more, they usually have less restrictive curfews (if any), may not have check in/check out times, are a much better place to meet other travelers like yourself. More than likely, families won't be staying at private hostels, so you don't have to worry about babies crying all night. But since there's no curfew, sleeping may be iffy anyway.