Yes, they do exist in many cities, but the setup varies. Some urban areas install dual-use trash bins that combine a normal public trash can with a dog waste bag dispenser and a small disposal opening. Others use pet waste stations that are separate from general trash bins, or place a dedicated dog waste bin right next to a public trash can.
The key is to follow local rules. In many places, bagged dog waste can go into a general public trash can, but loose waste usually should not. Always seal the waste in a leak-proof bag, tie it, and place it in the correct opening. If the bin has separate compartments for trash and pet waste, use the pet waste side when possible. Avoid putting dog waste in recycling bins, and do not use private or commercial bins without permission.
So, if you are walking your dog in an urban area, look for a combo bin, a pet waste station, or a clearly marked public trash can. If no suitable bin is available, carry the bagged waste until you find one.