Most buildings start with a ground floor and then move up with numbers. Basically, 1st floor actually should be second floor, 2nd floor should be third floor, etc.
While the old buildings are beautiful and fantastic, their age means that more often than not, there are no elevators. And often to get from one floor to the next, it means climbing 2 sets of stairs thanks to the high ceilings.
If staying at a hotel, try to get a room on the third floor. Why? It would be easy for people to climb up and break into the first and second floors. If you go any higher, you will die from exhaustion or have a problem in an emergency where you need to evacuate quickly. Rooms in the middle of the hallway are best. If beside the elevator, it will be noisy. Not the end of the hall for safety reasons.
When doing research on accommodations, pay attention to the reviews. I always avoid places where hygiene could be a problem (e.g. mentions of bedbugs, dirty sheets). Hot water is also a must (I have read reviews of places where hot water often stops running). Keep your luggage locked as much as possible, especially if you are staying at a hostel. It would be way too tempting for people to take something if your luggage is left wide open.
Make room in your luggage for a set of bed sheets and pillowcases. I am known as a germaphobe but I do believe this should be a practice for everybody. I use my own pillowcases even in five star hotels because you seriously never know and I would rather be safe than sorry. Having an acne breakout from the dirt and bacteria, being bitten by bed bugs, I could go on for a while. If you have room in your luggage, bring a double/queen size flat sheet so that you can fold it in half and use it like a sleeping bag between the blankets and the mattress.
Once you get your room, do a once-through of everything. If anything is damaged or missing, let the front desk know right away so that you will not be charged for it.