There are a number of cafes at the top of the hill and we stopped at the Café Lobkowicz which is inside the Lobkowicz Palace, near the North end of the Palace complex.
This turned out to be an excellent choice. It was quiet, close to empty (not usually a good sign, but today it was) and had an amazing view of the entire city from the terrace.
We each had a latte (90 kr ea) and shared a bowl of tomato soup (85 kr) and a grilled mozzarella, tomato and basil sandwich (195 kr). All were excellent.