Just got back from there. The main bit of Paphos is a bit too Brits Abroad for my liking, but once you get out of town its a really nice place. Get a car is my tip and find some lovely deserted beaches and drive to other villages for days out. Polis is very nice!
I'll second on Polis. I had a beautifully cooked swordfish at a quayside restaurant there in 1996. It also didn't seem to have too many Brits around. The coast is on the north side, so it might be a bit cooler. When I went to Cyprus in the summer it was around 35 degrees, though you may like that. If you do get a car, I would urge you to go up into the Troodos Mountains. It is absolutely beautiful up there.
If you like nice quiet beaches, try Pissouri, about 30 minutes east of Paphos, or go up to Apropdites Well, west of Polis. Nice restaurant above a steep climb down to a small beach, ideal for swimming.
Troodos mountains are worth a trip, some OK villages en-route.
Some nice bars in Paphos to the eastern end of the main waterfront - go to where the local drink - usually more classy than the main strip with all the British type bars. Centre of Kato Pahos (the tourist bit) looking a bit tired now.
Some nice drives in the mountains too. You will find some good restaurants etc tucked away if you like to explore.
Paphos is one of the worst places in Cyprus only superseeded by Ayia Slapper and is not a good indication of the real Cyprus. If you want to go somewhere that is Greek and not too many Brits a little fishing village near Polis called Laitchi
Pafos is a great place-of course there'll be Brits there but there are plenty of places where you can lose them-try leaving the tourist area and go exploring....you'll find hardly anybody there.
For a great little beach, hardly used except by the locals-right alongside the airport. Nice quiet little bay and although near the airport don't worry-they only have a handful of flights a day.
Enjoy it-it's a great place-this year was our fourth summer in Pafos and we'll be back in October if we're lucky!
Hire a car before you go and get iit for the whole time you're there-you'll then be able to explore the place.