Palermo is a walkable city, and most attractions are reachable by foot. If you are looking to save time, you can take the city's reliable bus or tram services. You could also hire a taxi but travel time may vary according to the traffic.
If you have more time, you can venture out to explore other attractions such as the beach at Mondello or the hilltop town of Monreale with its stunning cathedral, different museums dedicated to art and history or explore specific city neighborhoods such as Kalsa and La Cala.
If you have less time, you can consider combing some attractions or skipping some market to make sure you have enough time to sightsee or relax.