The remains at Limassol / Lemesos -- towards Episkopi -- (Kourio) are worth seeing, not quite up there with Paphos, but pretty good. There's an awesome roman site (prob the best in the region) just the other side of the Invasion border in Salamis which I saw when I was over this time (border re-opened 3 years ago, but it's still somewhat of a mockery), but it really needs a lot of work and restoration, the Turks have let it slip, I think most of the signs pre-date '74, and are showing the wear (i.e. in most cases they're either unreadable or ripped to shreds)..
On the subject of mockery, much of the old city of Famagusta fits that category... some grotesque "victory" statues and signs, ancient cathedrals turned into Mosques (imagine the uproar if the greeks converted a Mosque to a Church..) etc.. And Varosha is still fenced off, which is a sad sight.
There are also some remains in Larnaca (Kitium) which are worth seeing, and the other side of Limassol at Amatheus.
I like Cyprus, in the process of getting permission to build another place there (I co-own the current one), and once I have that I'll likely spend 9months or so in the year there.. perhaps more, but not sure I want to be reclusive all summer, and can't stand the heat, have to have the aircon going full blast. Outside of summer, it's a great climate.