It's recommended to rent a car for this itinerary as Palmdale is a scattered city with limited public transport options. Renting a car for three days will cost around $100-$150. Be aware of traffic during peak hours, and use online maps to navigate quickly.
If you have an extra day, visit the Aerospace Walk of Honor, where you can learn about the achievements of the men and women who helped shape the supersonic and space programs. You can also visit the Palmdale Amphitheater, a great entertainment venue for concerts and shows. If you have less time, consider visiting the DryTown Water Park and the Antelope Valley Mall only, which will take around 6-7 hours cumulatively.