This is a wonderful hotel in a fantastic location - it's about 200M from the foot of the Charles Bridge across the river from the old town - the neighborhood is called Mala Strana or Lesser Town, but there isn't anything "lesser" about this location. It's quaint, lots of stuff in close walking distance, and really old and beautiful.
The hotel has two buiildings and we stayed in the annex building which is right across the street from the main building where the lobby and restaurant are located - like a one minute walk. The annex building is quiet, has a lift, we stayed on the 3rd floor and our room was large (for European standards) and had a comfy king-sized bed and a large and clean bathroom. Everything one could ask for, and it was quiet.
Best part is the staff is excellent, we hired a taxi to and from the Prague train station thru the hotel, it was prompt and easy to do via email, and they were very helpful in pointing out places to see and just making the check-in process smooth and pleasant.
I'd highly recommend the Hotel Pod Vezi if you're staying in Prague, the neighborhood is way nicer than the Old Town, it's close to the Charles Bridge, Prague Castle, you name it. Lots of dining options including Lokal which is an awesome pub a few blocks away.
Last thing is a big shout-out to Bart working at the front desk, he was great and most helpful.