LUCCA: Best neighborhood to rent villa & Things to do/see

Be sure to rent a bike and ride around the wall. It is a narrow park with trees and is perfectly flat. Great spot for people watching, too.

I would suggest staying inside the wall, there are a lot of places on AirBnB, maybe not a villa, but you still can cook your own meals. We stayed here, with full kitchen access.
https://www.airbnb.com/rooms/1339380?guests=1&adults=1

The walk or biking on the wall around the city is very nice. Only about 3 miles with different points you can walk down to the city level. There are some very good reasonably priced restaurants. I would use an app like Yelp to find something that interests you. I was in Lucca for 2 days. I don't know if I personally could spend 5 nights.

Since you will be in Lucca for 5 nights, you may want to consider seeing some other cities during the day and in the late afternoon and evening see a little bit of Lucca each day. Pisa is only a 25 minute train ride and Florence is only about 1:20. I also think Montecatini Alto is a nice little village to visit if you would like to see a hilltop location and that is a 30 minute train ride. Just another option. Enjoy your trip.

Anywhere within the walls of Lucca would allow for easy walking, as that area is relatively compact. I doubt you'll find a villa in town, but an apartment should meet your needs. Rick's and other's guidebooks have good coverage of things to do in and near Lucca, as well as some good restaurant recommendations. Your apartment host will likely have an information package with other suggestions too.

What a wonderful plan! Lucca is a wonderful base (I spent two weeks there in 2017) and you are going to have so much fun.

As others have mentioned, to really get the best of Lucca it's best to stay within the city walls. There are a ridiculous number of rental apartments available so you'll be spoiled for choice.

As for cooking classes, I know a number of people who swear by the Extra Virgin cooking classes. I have a friend from Australia who visits Lucca frequently and does a class every time she comes. It's always a highlight of her visit:
https://www.extravirginlucca.com/classes

For what to see/do, here are some of my favourite things:

-Take a walking tour of the town. There is so much history in Lucca and, as helpful as the RS guide is, you get a lot more out of a guided tour, especially one done early in your stay (local guides are also great for restaurant recommendations!)
-Walk or bike the walls - this was part of my daily routine while I was there, as it is for many of the locals, in the late afternoon/early evening after the day trippers have gone home
-Climb one of the towers (on a clear day!)
-Grab a train (the station is just outside of the walled town) and spend a day in Pisa or the Garfagnana mountains
-Attend one of the nightly concerts at the Church of San Giovanni
-Visit the duomo and see the exquisite tomb of Ilaria del Carretto
-Brush up on your Italian with a half-day beginner language and culture course from the Lucca Italian School:
https://www.luccaitalianschool.com/courses-and-cultural-activities/a-taste-of-italian-language.html
(The reason I was in Lucca was to attend the school and it was an extraordinarily positive experience. I can't say enough good things about them)

Happy planning!

I've been to Lucca 4 times as my husband is from there. We always stay with family outside the walls, but he always says "one day we'll stay INSIDE the wall," so if you can do that, I agree it's a great choice. There are amazing concerts in Lucca in summer, not sure if they start in May (now that I think of it, I'm going to be in Lucca in late May too). Riding bikes on the wall is a must, as is going for pizza at Pizza Felice (it's a little hole-in-the-wall that his family has gone to since the 1950s). It's on Via Buia http://www.pizzeriadafelice.it/
You pay by the kilogram

We did two things in Lucca that were new for us and they turned out great. First, on our first morning we hired Wanda Martinelli to take us on a half day walking tour. https://www.luccatours.com/ She pointed out and explained numerous sights around the city that we would have never known about if not for her awesome tour. It was money well spent and it set up our other two days with great insights into the town. The second thing was a Puccini Verdi opera performance. They have shows every night and it was really enjoyable. They are in an old church near the cathedral. http://www.luccamusica.it/language/en/ I am not real fan of opera but love music but the show was awesome. I will admit it had rained all day so we arrived as the doors were opening for the show and we got a seat in the very front row, it was a great choice. They do various pieces of opera from the composers so it is not a complete opera which for us, non opera people, it ws just perfect. These were two things we did that championed our time in Lucca.

Wow...fun!! Your recommendations have been great! I think the 2 of us have started to lean towards renting a villa about 15 minutes from town because of the picturesque views and look of Tuscany we imagine only this region can offer. Plus, last year when we stayed outside of Cortona, Italy we did just that; stayed in a lovely villa and and it was a peaceful escape from "town." We understand we will need a car so that's hopefully not going to be an issue: Anyone have any experience renting a vehicle around Lucca? Do we need anything more than a U.S. drivers license?
We will also take the train or drive to Pisa and Florence for day trips - any suggestions?
From Lucca we go to Nice, France. Anyone been there and have recommendations?
Thank-you, pls keep replies coming.

you will need an international drivers license which is best purchased thru AAA. You can get majorly ripped on line if you search for one, they will offer all types for tons of money but basically the international license will be 20 some dollars thru AAA and its main function is to translate your US license to various languages for the police in the country you are using the license. Don't fall for online offers, contact AAA near your home and do it that way. The license also translates what DL restrictions you may have to the country in question. I didn't get one for English speaking countries but for our Italy, Austria, Germany trip I got the license. If it were me I would take the short train ride up to Pisa rather than drive and try to find parking, but I only took the train to the Pisa airport in and out.