If your ambition is to climb Cuba's highest mountain, Pico Turquino is your answer. It can be trekked from the south or the north.
From Manzanillo, you might consider staying at the Farallon or Mareo Del Portillo hotels, and travelling to Las Cuevas, to the east, where the entrance to the park is found. Alternatively, you may want to get yourself closer the night before, staying at the campgrounds to the west of Las Cuevas.
A small building on the road marks the entrance, where you will find a guide who will take you up the 11 hour trek through cloud forest and lucious vegetation. From the south, the trek is a little shorter, but steeper. Plan to camp the night on the mountain and take warm clothes as the night can be cold. They say on a clear night, you can see the lights of Haiti from the top.
For approach from the north, see my "off the beaten track" tips for Bayamo.
At land's end south of Manzanillo de Cuba is the little fishing village of Cabo Cruz. It is a nice spot to check out, since it has a wonderful example of a Spanish lighthouse, built on a Spanish colonial base. There is a little museum there, and active lobster fishing industry, and even a modern windmill. While the officials will tell you there is no restaurant, if you wait around, you will soon be approached by someone offering you a lobster dinner in their house. If you are not willing to take the offer, make sure you take food with you, as there are no restaurants along the way.
Note that the hiking trail known as El Guafe is three kilometres back on the road.
Travelling south from Manzanillo, or west from Marea Del Portillo, you reach an area of Cuba that is little travelled by tourists, but is one of the most fascinating natural corners of the country. Most of the area is the National Park of Desembarco del Granma, named after the point of desembarkation of Fidel and his revolutionists from their boat named the Granma. (About 25 km SW of Nequero)
The main features of this park are its 20 caves and series of stepped limestone terraces, as well as some of Cuba last remaining untouched rainforest. One of its caves holds the famous "Idolo Del Agua", an aboriginal Idol carved in the stalactite. A two hour marked trail, named El Guafe, is an easy entry point, although you have to watch very carefully for the entry sign. It would be worth finding a guide to give you more detail on the area, either at the gate or in the little Village of Cabo Cruz. Here you will find a variety of birds, cacti that are said to be 400 years old, and many other indigenous plants. Any guide book will give more detail.