Cyprus, for the most part, is a very safe country where people can walk freely on their own without fear of being attacked or robbed.
In the large cities of Limassol and Nicosia, there are some areas which are best avoided late at night, but in the tourist resort towns of Paphos and Larnaca, the only real danger is avoiding drunken tourists in peak season.
In the sleepy towns like Polis or way up in the mountain villages, there is absolutely no danger at all.
As for cleanliness, Cyprus is a modern country but sadly, people think throwing rubbish out of car windows or dumping rubbish over the side of a hill is perfectly acceptable. The authorities regularly clean the roadsides and there is a large fine for dropping litter on the motorway, but like many Mediterranean countries, throwing litter on the floor rather than into a waste bin is part of local culture.