Hi Colette.
Great choices for your trip.
I live in W. Canada, and usually fly home from Florence if my trip ends near there.
You flight from there will connect in Munich or Frankfurt, if you're flying Air Canada/Lufthansa.
Be aware that flights from Florence are often late leaving there, and they never tell you why!
So if you went that route, you'd need to make sure you had a connection time of at least two hours in Germany, or wherever you connect to.
You can do the same for Pisa, as there is a direct bus to Pisa airport from Lucca, taking about 25 minutes.
We were just in Lucca in September, and stayed slightly outside the wall, but an easy walk in of about 15 minutes; less if you have better knees that I do!
Also, only 10 mins walk to the train station.
We stayed at "Granny's House".
Here's the link:
Located in Lucca, near Piazza Napoleone, San Michele in Foro and Guinigi Tower, Granny's house has a garden.
www.booking.com
Long link, sorry; but you can find it on Booking.com.
It was really hot weather when we were there, but the house was nice and cool due to nice tile floors, and good shutters.
The only thing is that it does not have a washing machine, but you can hand wash and there is a drying rack to put outside.
We saw a couple of laundries along the road if you needed them.
The little kitchen and bathroom are nice, and it was really clean.
It's got a little patio out back, and is all on one level.
Lots of little shops and café- bars along the road, and a huge supermarket not far away.
We were also in Rome, and stayed here:
Right in the heart of Rome, situated within a short distance of Santa Maria Maggiore and Vittorio Emanuele Metro Station, Around The Corner Colosseo B&B...
www.booking.com
Also on booking.com:
Called "Around the Corner Colosseo".
We thought it was just a room, but it turned out to be a huge 3-bed room, and a kitchen, and a nice bathroom.
No living room, but an easy chair in the hall.
It was all so clean, it squeaked.
And fabulous sheets!
You can't use the stove for some safety reason, but there's a microwave, coffee maker and kettle.
It was walking distance to Termini Station, about 10 mins.
Near buses and Metro.
The sisters who run it are fabulous women, and couldn't do enougoneh for us.
They live in the building.
I'd stay there again in a heartbeat.
If you need more info, let me know!