We stayed in the apartment next door to the B&B (same owner). It was lovely. Three large bedrooms, a fully functional kitchen and dining room, extremely clean and comfortable. My teenage daughter needed a break one day and just stayed in the apartment by herself, happily. It's maybe 1/3 mile from the gates to Old Town (best way to get there is to walk up to Rue Saint Jean and then turn left) but also plenty of restaurants even closer. Caroline was extremely helpful with everything.
Charming and sweet, but if you MUST have privacy, choose a modern hotel. Caroline is a most gracious hostess! The soft pillows were divine! This is exactly what I would say to any friend of mine.