Do you need a car in Puglia/Basilicata area?

There is some public transportation in Puglia. But unless you augment the trains and buses with some sort of bus tour (which puts you on the tour company's schedule), you are not going to cover ground as efficiently as you can with a car. If you're accustomed to having a car when you travel to more rural areas, I think you're going to really miss it in Puglia.

I stayed in Lecce (a lovely city) in 2015 and found a travel agency (which I assumed was the local government tourist office, but it apparently was not) that ran van trips to multiple smaller places at a very reasonable price. I think it was about 60 euros for a full-day trip. These were not tours; they were just transportation to far more places in one day than one could possibly manage by train and bus. The trips were not pre-scheduled; they were based on demand, so it was helpful that I was able to hang around Lecce for several days and hope for the best. In the end, I was able to take three of the trips. Every time I try to find those trips online I end up wandering all over the Internet; today I can't find them at all, which doesn't necessarily mean they are not running. I assume the cost would have to be quite a bit higher now because of gas prices.

I suggest some online research to see what you can find in the way of one-day tours/trips you could use to supplement public transportation. Perhaps you could do part of your sightseeing by public transportation and rent the car for just three days--though I know a 3-day rental may not be all that much less expensive than a one-week rental.

To see whether towns you're interested in have bus service, you can start with Rome2Rio.com. You'll need to keep clicking through the website to find the name of the bus company and go to its website for accurate schedule information. The fares, frequencies and travel times displayed by Rome2 Rio itself are extremely unreliable and could lead you seriously astray.

You really do need a rental car in Puglia/ Basilicata because a lot of the points of interest in are the smaller towns of only a few thousand residents ( ie Alberobello, Locorotondo, Otranto, Gallipoli) and some spectacular beaches in locations outside of towns. Local buses are on a skeletal schedule to some of these rural spots, sometimes only running once every few hours.

As an example, it takes about an hour to drive from Matera to Alberobello. The same trip on the bus takes close to three hours. That means you will have a hard time getting to more than one— at most— two places in a day. With a car. you can see three or four locations in a day and it will be easier to move on to a different town from which to base yourselves as you move through the region.
To find a car rental for less than $700, you might try Rentalcars.com or Europcar.com which list many car rental agencies in Bari, Lecce and Matera.
Have a great Trip!

There are local trains and buses throughout Puglia. It takes some planning and basing yourself in places that offer the most options.

Think about more than one base. For central and partially southern Pugia, I'd suggest Lecce. Bari might be a good base in northern Puglia. With a little research you'll find you can get around quite a bit of Puglia without a car. It may take more time to get to places, but it can be done.

I have been to the area twice and had no problem getting around throughout the area using public transportation. The only difference between Puglia/Basilicata and other areas of Italy is that some of the train stations were closed due to lack of ridership and tickets had to be purchased in the towns, so you do need to plan ahead.

It is completely dependent on where you want to go and how fast you want to get there. Also, where you want to stay matters. Obviously if you wanted to stay at a masseria, you would need a car for example. Sometimes, the train station is outside of town, Ostuni is one example.
I wanted to go to small villages and do outdoorsy things, all at my own pace, so there was no question I was going to drive. Plenty of people have used public transport and had successful trips, most likely supplemented by a private driver on occasion.
Have you looked at the schedules?
Share where you want to go and we can better advise. Also, any personal details about yourselves can help: If you are generally an early riser and fairly organized about juggling multiple train/bus operators, you'll have an easier time. Also, if you have no issue paying for a driver when needed, that can help.

We did Puglia in Oct. No car. Used trains and buses and once a taxi. A car may have been nice. Nowadays you want to look at the cost of the car.
Some people want to see 2-3-4 places in one day. For us that is too rushed type of travel. A ping pong way.
It is certainly possible with no car and often a car is an impediment due to parking. Then again, if you are just rushing into a town for a couple hours, then OK.
You may have to plan more for trains and buses. Wait more, spend more time to get A to B. We all know that. You know that with your experience. So, it depends on what you want to see.

Well, now that you’ve gotten plenty of opposing views, I’ll add mine to the car rental side. A few years ago, we did a trip like the one you are planning. I would have been happy to rely public transport, but my research showed me that having a car was much more efficient. Even where there were buses, the schedules didn’t suit our plans. You could do as I did. Lay out an itinerary; then look up transportation schedules. That will give you concrete information for making your decision.

My answer is yes unless you limit your itinerary to towns on train lines but then you will miss a lot.

thank you everyone! I think we will have to bite the bullet on cost and rent the car!