There is only a parking garage close to Haarlem Central Station, but there is a free public parking lot at Haarlem Spaarnewoude station (east of the city).

If you want to travel on Saturday that will make it a bit easier since there is less traffic. Only not in the center of town, people will be shopping. So expect it to take you a while to get to one of the parking garages and there's always the (small) risk of it being full, so you have to wait for someone to leave.

It's still a doable trip, only I feel it's so much easier and quicker going by train :-). But if you include it with other destinations a car might be your best option....

If you want to fill your day you might also consider stopping at a few more places like Zandvoort (to walk along the sea) and Volendam (a quirky touristy place). And if the weather is nice a ride through the area around Loosdrecht is really beautiful. Al within 30min from Amsterdam.