Four bases, and they differ mainly in how much company you want: the backpacker end of Don Det, the quiet side of the same island, Don Khon over the bridge, and Don Khong, which barely notices travellers at all.
Don Det, the northern tip
Where the boats land and where almost everyone stays: bamboo bungalows on both banks, bicycle hire, banana pancakes and the island's only real concentration of bars. Rooms range from a fan box with a shared bathroom to a river-view balcony with a hammock, and the difference in price is smaller than you would expect.
Don Khon, over the bridge
The larger island south of Don Det across the old French railway bridge. Same hammocks, fewer of them, more families living ordinary lives around you, and Li Phi Falls on your doorstep. Choose it if the point of coming is quiet; you will still be a fifteen-minute cycle from a beer on Don Det.
Don Khong, the big island
The biggest island in the archipelago and the easiest to reach, with a road round it, guesthouses and small hotels in Muang Khong, and almost none of the backpacker scene. It is the sensible base if you are travelling with children or want a room with air conditioning and a working generator.
Nakasang is not a base
The mainland village where the buses drop you and the longtails leave from has a market, a few guesthouses and nothing else. Only sleep here if you have arrived after dark and cannot get a boat; the crossing to Don Det takes about fifteen minutes and boatmen stop working in the evening.