Hostels, so just a bed in a shared room is likely the least expensive.
Hotel and hostel booking sites will help you find them. Search online for 'hotel' or 'hostel' and name city to find booking sites.
Do double check on other sites for reviews. And check you can reach the location on the day, as some days public transport may be limited.
If you want private rooms, those same sites can help you as well but prices will be higher.
To get cheap accommodation at Christmas you need to book far ahead, as it is about a week till your travel date you will have to take what you can get.