If you're in Luxembourg on a Saturday, check out the weekend markets. In Place Guillaume, you'll find all sorts of fresh fruits, vegetables, meats, cheeses, and breads. There are about 20 to 30 different stalls set up, and the merchants are open for business from about 9am to 2or 3pm. A few sellers offer homemade jams and various specialty foods, like salsas and sauces.
In Place d'Armes, expect all sorts of antiques, books, and a few homemade crafts. Different sellers display china, silverware, stamps, coins, and various collectibles. I admired some great bamboo purses and Asian jewelry, and I couldn't resist buying a bag of fresh, hot sweet peanuts. These merchants are also open around 9am, but stayed longer than those at Place de Guillaume.