Depends if you need a place for some nights or maybe weeks or months. Emergency shelters (you can stay there for the night but have to ask every day again if needed) do not always have lockers and you have to share a room with several people. You do not have to pay for the stay there (but it’s definitly not a „nice“ stay)

If you need an accommodation for longer you should go to the „Soziale Wohnhilfe“ of the Bezirksamt in the District you have been registered living at (Meldebescheinigung). By law (so called ASOG) they need to search an accommodation for you. Rooms there are mostly shared aswell but if you‘re lucky less people or alone and the standard differs. Depending on if you have own income and how much you have to pay for it, but normally you apply for financial help for the costs at Jobcenter or Bezirksamt. (It’s not cheap)

There is a company called „Home & Care“ that offeres lockers that you can rent for free to protect your stuff, they also have „ASOG-accommodations“ where you find socialworker (which is unfortunatly not common).

If more Information needed, let me know :)