Al Ain is a spread-out city built for cars, and getting around on foot between sights is not realistic except within the oasis itself. Taxis are abundant, inexpensive by Western standards, and the most practical way to reach the fort, museums, zoo, and camel market from wherever you are staying. Drivers generally know the main attractions by name, though having addresses written in Arabic helps for less obvious destinations. Ride-hailing apps including Careem operate in Al Ain.
The main sightseeing cluster — Al Jahili Fort, Al Ain Museum, Sheikh Zayed Palace Museum, and the oasis entrances — is compact enough that you can walk between them if you are comfortable in the heat. Jebel Hafeet requires either a rental car, taxi, or bicycle for the summit road; taxis will take you up and wait, which is a reasonable option for a sunset drive if you negotiate a return fare in advance. Hili Archaeological Park and the camel market are both short taxi rides from the centre. There is a local bus network but it is infrequent and not practical for tourist sightseeing.