"March" — Two weeks in Puglia in March (and early April) has been our favorite region to visit in Italy in spring so far. We’ve spent several weeks in Puglia off-season on two other trips.
"dead with not much open” — Puglia is not even slightly dead in March except for the beaches and some of the beach towns.
"weather wise" — The weather was either warm or pleasantly cool every day we were there.
"3 locations total" — For the three, I suggest Lecce for the city, a seaside town like Trani, and staying in a trullo (like a stone igloo) in that part of Puglia (i.e. near Locorotondo, Cisternino, Alberobello). Do a day trip to Matera.
"take it slow" — The towns (although not the restaurants) close down midday and early afternoon, so it’s the perfect time for a long lunch and for people-free photography in the historic town centers.
"beautiful landscapes" — We did not even try to see the beaches that are surrounded by rocky cliffs, but they are there, as are the olive groves and the countryside dotted with trulli (both ruined and renovated) and the harbors full of colorful wooden fishing boats.
"architecture" — You won’t see trulli anywhere else in Italy and you will enjoy the exteriors of the small Puglian Romanesque churches and the Baroque churches in Lecce (carvings of animals, monsters, flowers, people cavorting with no obvious connection to anything religious).
"yummy food" — We’ve spent more than 365 days total in Italy, love eating the most local possible food, and we find the food in Puglia second only to that of the hinterlands of Liguria (in spring, you will eat things like fried wild hyacinth bulbs and wild-harvested greens).
"off the beaten path" — Puglia is not in any of Rick Steves’ books and is only popular in the summer (although Easter weekend was busier). You will need to fly into Bari or Brindisi from Rome (or another European city), or take the train from Rome, or drive from Naples. Puglia does not have any world-famous sites or artworks and is definitely easier to see by car, so this helps it be less “beaten."
"rent a car" — Puglia is a good region to drive in and to park (outside of the ZTLs, of course, but the old centers are small and it’s just a block or two to walk in from parking spots).
"towns that are smaller but still have options for restaurants" — The old and car-free center of Ostuni (for just one example) had three of the best non-fancy restaurants we’ve been to in Italy within a 5-minute walk from our apartment. Lecce had several excellent restaurants and also a cooking school called The Awaiting Table (https://awaitingtable.com/cookery-courses-italy/) with half-day classes.
"not big into hiking" — Nope, no need for any hiking and even the hill towns are on little hills compared to Tuscany's and Umbria’s.
Search for "Puglia" in the Italy Forum for details of towns, restaurants, etc.
