Lucca

Lucca is largely traffic free for the majority of the center of town. There is a ring road and parking garages on the edge of town but that's pretty much it. I'd double check the parking situation with wherever you want to stay - listing where to park and how close it is are commonly listed items. Be sure you have a plan and know which gate and where you are going as you approach and enter the city. I have seen scared tourists inching past tables in cafès and driving on top of the walls. Do not put yourself in this position.

As you would expect walking is the usual way of getting around town so it is not a place where you can expect to drive places or get a cab. But it is also 20 minutes side to side and about 15 minutes top to bottom to walk at brisk pace so it's not big and there are many places to stop and sit as you head places. And it is entirely flat unless you decide to walk up to the walls that surround the town.
That being said there are cabs that can navigate the larger streets so in a pinch you could call one if needed.

Also be aware that the traditional architecture of Lucca was a ground floor tall enough for carriages so the "first floor" - which is not the ground floor - is often 32 or so steps up. So probably equivalent to second floor climb in the US for the "first" floor.

Have a great visit,
=Tod

Basically the entire Centro Storico is a ZTL. Hotel guests can enter in Lucca ZTL for loading and unloading luggage but it the responsibility of the hotel to notify the authorities with the license plate number of your vehicle each time the ZTL is entered. Any visiting within the city would have to be done by walking.

As folks have mentioned, you pretty much can't drive in Lucca's historic core. A map will show you all the parking outside the walls. The train station parking (south) is gonna be closer to the Cathedral and the big piazza surrounding that. There is a lot of parking on the north side that would be closer to the old Anfitheatro, the tower and the gardens. So your choice depends on what is most important from a convenience standpoint and whether you can arrange transport from your parking spot to your hotel inside the wall.

Could you bring a wheelchair for him?
Or rent one there, perhaps.
As far as I remember there are many pedestrian only streets and as someone else said, it is entirely flat throughout the town.
The top of the wall is also flat, car free, and there are sloped roads and paths to get up to it.
Lucca is just charming, it would be a shame to miss it!

This isn't an endorsement but San Luca Palace inside the walls in Lucca and lists a private parking lot as one of their features. They are positioned just on the edge of the town where traffic is allowed in via Porta Sant'Anna. You might reach out if you are interested and they have your date and meet your budget guidelines.

Good luck,
=Tod

Hotel Ilaria on the opposite side of town from San Luca Palace has parking as well