The Valdanos beach (Plaža Valdanos) is located in the harbor a couple kilometers from Ulcinj. It's covered in pebble, including the sea entrance. You may encounter arge rocks and sea urchins, though, so bring special footwear with you. All the usual infrastructure (shower, changing rooms, toilet, shezlong rental) is there, as well as several cafes.
You can get there by foot, going northwest from the city through the olive grove, or by car — there's a paid parking nearby.