Nice town near Amsterdam airport

You'll like Haarlem. Some 30 mins from Schiphol by direct bus (leaving from the railway station) or train (with one change).
Alternatives are Leiden (even closer to Schiphol with perfect train connections and a couple of trustworthy hotels at 5 mins from the railway station) or Utrecht (also around 30 mins from Schiphol by direct train). All three are pleasant historical cities.

We will have the car for our last night, returning it to the airport the morning of our flight. So we're looking for a town where there would be a hotel with free parking. We could be out of town a bit. We've looked at Haarlem. It does look lovely, but none of the hotels seem to have free parking. We're hoping for our drive to the airport, the next morning, to be under an hour.

With a late morning flight (11 ish?), and getting to airport 3 hours prior, you might want to consider getting rid of the car the night before and taking train to Amsterdam for dinner and hotel. Then no hassle the next morning taking train to airport. Or taking bus from airport to Haarlem for dinner, hotel and bus in the morning. IMHO, less stressful than returning car in the morning.

The sensible thing to do is indeed returning the car the day before, and use hassle-free public transport to get to the airport. Bus 300 leaves every 10 mins or so from Haarlem station. Nothing to worry about. No possible delay at the car rental to reckon with. No possible traffic problems during rush hour to reckon with.

Thanks for the suggestions. We're not very sensible. I'm sure we'll figure something out. My husband loves to wing it.

I have a suggestion: the Amsterdam Aiport Mercure has on-site parking, and very easy access off the A10 highway. It is very close (3 min walking) to a nice lake, and it has easy transportation access to Amsterdam central areas if you want to go there at night.

You will not find centrally located hotels, in the heart of towns and cities, in that regions of the Netherlands that have free parking, and even on-site parking is tricky except for the more high-end ones. Get over the free parking and just sum up the parking fee to the price for the night.

Your second best options are hotels in the Zuidas area, also just off highway, which is a sort of satellite center that has some things going on at night and easy subway access elsewhere. It has a handful of fancy restaurants that now open for dinner as well. No canals or old buildings though, everything there is built after 1978.