Lastovo gives you a exellent cycling tours.
For less active cycler only the area of Passadur and Ubli is recomended.
But if you are in a good shape there are nice tours over whole island. The roads go up and down. Take a mouting bike gear with you. The highest hills on the island are over 400m high. There are also some lonely dusty roads to lonely bays and places with a great panorama views.
Buy a touristic map of Lastovo at the local souvenir shop- there are all roads in this map.
It's difficult to find a secluded spot if you don't have a boat, but you can find a tiny beach near Zaklopatica (see the "Hike" tip).
There is also a cement dock of sorts near Lastovo village called Sv. Mihovil.
Swimming looked to be easier around Pasadur.
In summer, hire someone to take you to the smaller islands offshore.
I enjoyed walking from Zaklopatica to Lastovo village; climbing "Hum" (there are two access points to the 2 km trail on the main road); walking aroung Lastovo village; and walking along the coast. Unlike other Croatian islands, it is difficult to find coastal paths. There is one in the cove adjacent to Zaklopatica.
In some areas (near Ubli, Pasadur) it is advised to stay on the marked path. Lastovo had a military installation on it so heed that advice in those areas. Near Lastovo village, Zaklopatioca, and Skrivena Luka, no worries.