The best place to stay depends on what you want and what your budget is.

There is accomodation downtown Labuan Bajo but around jalan Soekarno Hatta it will be very busy. Other homestays and hotels are spread around town which can be less convenient if you don't have your own transport (although some hotels have their own car of minibus with or without payment). Then around Waecicu Beacht north of Labuan Bajo and Pede Beach south of town where you also need transport. Bear in mind that there are no taxi's in Labuan Bajo, there is Grab but ojek (motortaxi only).