Cyprus feels incredibly safe and exceptionally friendly towards solo travellers, and is a wonderful place to enjoy an abundance of historic sites, art and nature.  Parts of the coast are full of nice hotels and palm trees (although you could be anywhere), but within minutes on the bus or in your hire car you can be up in the mountains, in a monastery or exploring a Roman villa. After I had visited the main sites that were on my list I just started following any brown sign depicting a place of interest,  That took me to beautiful dams and hidden neolithic settlements, for example. 

Cyprus is a particular haven for lovers of all types of art but perhaps particularly those who make and/or love mosaics.  Many ancient mosaics have only been discovered relatively recently and are presented well, showing off their brilliant execution and remarkably bright colours.  Others are there underfoot as you wander around ruins in the sunshine.  In the monasteries they are everywhere, dazzling with gold, and so abundant that sometimes you just don't know what to look at first.

At the Sanctuary of Aphrodite I was thrilled to meet the site manager who showed me the beautiful original mosaic of Leda and the Swan, which had been discovered there, and the reproduction thereof, which he had made with his father when he was 15.  Spot the Difference for creatives!  Sanctuary of Aphrodite at Palaipafos (visitcyprus.com)