Both of those are superb properties. If you book at Lama di Luna you must ask them to book you a table at Antichi Sapori in nearby Montegrosso. And if you are there more than one night, you should eat either in Minervina Murge, known locally for good food, or as Masseria Barbara. The latter is fabulous for Sunday lunch.

You must book both hotels asap. Torre has a sister property (Torre Coccaro) which is also lovely, but we like TM for the very large pool and for the incredible breakfast buffet, not to mention the lovely rooms. You do have to drive at night for great eating, though.
The very best places to eat are a little distant but there are plenty of options nearby.
They get a lot of bike tour groups so contact them as soon as you get your dates.

I wrote two trip reports and if you can't find them I will link them here. We've been to Torre M on other trips but I did not write a report.

Let me know what else you need. I hope to go back before too long.

We're going to try for four nights at Torre Maizza and four at Torre Coccaro, space permitting. We'll have either lunch or dinner at Antichi Sapori right after we get off the train in Foggia. Yes, there will be driving involved, but that'll be fine. Your trip reports were great. Thanks.