Nothing you mentioned is that far away.... all easily driven to from AMS in less then 1 hour. Traffic in Amsterdam itself can delay you a bit though, so renting from AMS Airport might not be such a bad option, it's adjacent the freeway.

I wouldn't take the car to Haarlem. Parking is costly and Haarlem is an easy stop by train or bus. The Keukenhof is also a direct bus trip from AMS Schiphol airport (combi-tickets are available) or even Haarlem. Going here by car is easy as well.

So if you have a car you might be better of really driving through the countryside......especially if the weather is nice.