Fully booked hostels

Hey reddittors of Hamburg

Me and the gf decided to impulsive skip work and head to Hamburg for the weekend. We’re currently in the bus 4ish hours away and we’re looking for cheap accomendations for two nights but it turns out most of Hamburg is booked. Is it worth to pay 100 euro a Night or do you Think it is possibly to find it cheaper strolling out the City and asking hostels/hotels? Also if anyone knows cheap not fully booked hostels Best regards The excited Dane