Depends on what activity you like to see.
If its sights you want to see then maybe hire a car for couple of days (around 40 euro per day local hire) and you can se most of the island.
The "ghost town" of Famagusta,go to Lefkosia and cross the border into Turkish part of town,Troodos mountains,old sites around Paphos.
Anywhere you go will be advertised for things to see.
Nightlife I cannot tell about except that Ayia Napa is a very popular place for nightclubs bars etc.
I was in Larnaca recently and don't recall seeing any special events advertised.
Get there and look around there will be much to see for all tourists for your stated time.
VTRS here will give more details than I have but 2 days is not much time to explore this lovely place
By the way it will be HOT
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