Agriturismi tend to be less on the luxury scale. After all, they started off as farm-stays, so it's fair to say that they're not the most luxurious.

As for the location, I'd rather look for Tuscany - and my absolute favourite, Val d'Orcia - for a villa (of which there should be plenty). The reason is that E/R is either flat or hilly; the flat bit, in November, might already be quite foggy in some days and, to be fair, it's not the most stunning place where to celebrate a new baby! The Appennini hills aren't bad, but I find Tuscany a bit more, shall we say, cinematic. Especially Val d'Orcia.