There is nothing to do at Mia Moja na Moja except:

eat (masses of fresh fish and vegetables, sometimes fresh crab fished from the mangroves, lots of fruit), 

read, sleep (these two activities can often be interchangeable as you lie supine on the Lamu swing beds wafted by the breeze and occasionally opening the eyes to gaze at the ocean), 

walk on the beach – at dawn, at dusk, at midday, at any time as the beach is always changing shape and colour, 

swim (sometimes in calm pools left by the tide and sometimes in rougher water), body board, bird watch, play games, run (if you really have to)

visit Lamu Town

take a trip to the mainland and visit the local farms on the back of motorbikes

swim with dolphins

snorkel round the coral island out in the Indian Ocean

dhow sail round the island and go deep sea fishing.