It really depends on what you're looking for. If your idea of a rest day is dashing around visiting the many interesting sites such as you might encounter in a Pamplona or a Burgos, you might be disappointed, since the biggest city is Cahors, with only around 20,000 people. Conques, for example, is a cute place, about 10 days in, where many people stop, and the Abbey is wonderful, but the whole town is around 500 meters long, and after exploring the Abbey, there's not much to do other than kick back and relax. Ditto with the other larger towns: Figeac, Cahors, Moissac, etc., along with many smaller places which are wonderful, such as Auvillar. All of these towns will have interesting things to see -- churches, small museums -- but after seeing them, you're mostly going to be hanging out. Resting. Which is fine, too, of course. That's the beauty of the Podiensis. It's serene all the way. But big action there ain't. I would pick through Miam Miam Dodo, or Dave Whitson's new guide in English for ideas, and figure out what interests you. A stay in a pleasant chambre d'hote in the middle of nowhere could also make for a great rest day. With the emphasis on rest.
(Like others who have commented below, I'm also a proponent of taking an extra day when you find a place that you like -- and letting the Camino come to you, as it were -- but I understand this can be difficult if you've got your itinerary programmed out).
My wife and I took only one full rest day, and that was in Figeac, from which we took a local train to explore the wonderful medieval hilltop town of Rocamadour. It wasn't actually very restful, but we enjoyed Rocamdaour.
I expect
@Pelerina might chime in. She's living in Lectoure, and always has good specific suggestions.