There are two major international airports in Cyprus: Larnaca and Paphos. Many international airlines fly into both airports including British Airways, KLM, Cyprus Airways and some regional airways from the UK (operational through the summer months only).
Larnaca is situated in the South-East of the Island and so is the airport recommended for exploring the areas from Limassol to Larnaca to the FREE Famagusta and Nicosia areas.
Paphos is located in the West and serves the area around Paphos up to the Polis/Chrysochou area on the South-west side of the Island. As Limassol is equidistant to both airports, you have a choice of which to use.