We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water as a solvent for nonpolar (inert) molecules. Water molecules are of the ``Mercedes Benz'' type, i.e., they possess an equilateral triangle symmetry, with three bonding arms. Bond formation depends both on orientation and local density. The insertion of nonpolar molecules (no bonding arms) displays the qualitative features that are typical signatures of the hydrophobic hydration: a large negative transfer entropy; a large positive transfer free energy; a steep temperature dependence of the transfer entalpy and entropy, i.e, a large positive transfer heat capacity. In order to understand the microscopic bases of the hydrophobic effect we include the analysis of the hydrogen-bond coordination of a water molecule in the bulk and in the first hydration shell. The results are compared with experiments where possible. The finite temperature analysis is carried out by a generalized first order approximation on a triangle cluster. In the very last part of the talk we briefly introduce a work-in-progress application of the water model to the study of the hydration of a polymer (SAW on a triangular lattice) by means of Dynamic Monte Carlo methods.