I am considering a trip to Apulia in November.
I don’t want to tie myself to a itinerary and i don’t speak Italian. How much trouble will i have finding lodging?
Monopoli, Ostuni, Lecce, Albrebello,
I'd feel comfortable taking that risk in November. You might check to see if any have special events or festivals that might put accommodations in short supply, but otherwise probably fine to book on the fly at that time of year. I use Booking.com for convenience.
Of the four places you list, the only one I would not choose is Alberobello, rather touristy.
You'll be fine in November!