The Northern Turkish side is extremely safe no war has been on that side since 1974, Turks are very hospitable hosts and have fantastic cuisine, the food is absolutely delicious and the Northern beaches are amazing.
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Your question at first glance may seem a little ridiculous, as it depends on the weather in each particular area. However, the eastern coast tends to be 3 - 4 C warmer than Paphos in the West. You could expect temperatures averaging high 20's during early May in Paphos, lovely temperature with little chance of rain.
Generally speaking, it is cheaper to travel in Northern Cyprus than it is to travel in the southern part of Cyprus. Car hire, resorts, and dining tend to be of better value in the north.
The political situation is somewhat tense, but not violent. Crime numbers are relatively low for a European destination and statistically lower than those in Southern Cyprus.