Cyprus is not cheap... definetely more expensive than Portugal, but you can get by... depends what you wanna do!
I'd suggest you goto Limassol rather than Nicosia. It has a wider expatriate population, seaside, easy access to the mountains, relaxed life and I'd figure just as much to do as Nicosia. Rent in Nicosia I think is more expensive but apart from that, theyre practically identical price-wise.
Things to do ermm off the top of my head (in Limassol):
2 Waterparks
2 Bowling Centres (Space Bowling is excellent)
4 Cinema complexes (Othellos, Cineplex, Rio)
3 nightlife areas (Galatex, Enaerios and Lanitis Mill)
Some nice beachside bars/cafes.
Lotsa food places.
Shooting club is up the mountain a bit, but good.
Elias Country Club (green bowling, horse riding etc.)
Waterspots and lots of'em
The beach of course....
Trips to Troodos Mountains, villages...
Close to Paphos, which is real nice.
Lotsof shops,brand names etc. if thas what you're into....
Can't really think of much else but sure there's some stuff you can figure out.... oh and paintball
Go-karts!
Have fun!