We are going to Pernera, Cyprus in June 2018 and would love a trip into Northern Cyprus and Famagusta. Scunner, did you hire a car or did you go on an organised trip?
Somewhere between the two - there was a taxi kiosk outside our hotel and they were advertising excursions (I don't think anyone could struggle to find this excursion, it's advertised all over). Anyhoo, when we enquired about the advert at the taxi kiosk, what do you know, the lady at the kiosk told us her husband was a taxi driver who did private tours to TRNC/Famagusta.
His price was the same as the tour busses and they have the nice stretch merc taxis there (three rows of seats, three doors per side) so we decided to go with him. It was great - lovely and spacious, air con, he took us first to Salamis (photos below) then Famagusta centre, then the forbidden zone/beach. Unlike the bus option he gave us tons of local info and then sent us off to explore - no return time, no schedule, we moved on when we had seen enough.
I'm sure there will be this option in most resorts - I'd recommend it.