Lucca

Good choice. Use Booking.com to find an apartment as they have good search filters and verified reviews. If you'll have a car, get a place with parking outside the ancient city walls but within walking distance of the center. If no car, stay withing walking distance of the train station. Do a lot of research as it's a great city and area.

I would stay within the walls for the best experience. I stay at the Ostella San Frediano in Lucca. It is a converted convent. Very clean, basic accommodations and a good location inside the walls.

Stay inside the walls. It is a small town so staying near the train station is no advantage. We rented an apartment with 2Italia which we loved.

Rick,

Holiday Lettings has many 2 bedroom/2 bath apartments for around a hundred dollars (US) a night. You don't say the makeup of the 4 travelers so if the second bathroom isn't a necessity, the nightly cost could be even less.

Be sure you get a place with air conditioning. That may not be an issue with apartments in Lucca, but don't assume it's there if it's not specified in the listing.

hi rick
i agree with luccaholidayhomes.com. they have a 2 bed/2bath, ground floor, A/C, garden. you say for 4, don't know dynamics, there is a sofa bed in living room. within the walls and near transportation. do you plan on getting a car at anytime? if so, don't forget an IDP from AAA and if parking available, free or a fee, how far away. there are other apartments for rent, some with lift/elevator or steps, just concerned that you said your wife is on oxygen. if you decide to stay here, luccatours and extravirginlucca.com also pinocchio's hometown is near in collodi. there is garzoni gardens and the butterfly house,and beaches to take bus or train. let us know how you do please
aloha

Lucca is a nice little city, but it can be done in one or two days. Of course, you can use it as a base for visiting other places. Personally, I would choose Florence for such a base.

We have used Lucca as a longer term base for us and thought it was the perfect location for extended stay. I'm not a fan of Florence.

We are more small town (compared to Florence) people. Knowing we can train or occasionally rent a car for side trips.
Thanks everyone for your feedback