I like to go for a walk on holiday(mad dogs and all that,although I'm Scottish so it saves on a bus fair ) but walking in that heat can be very hard on you.As you've never been to Cyprus it's a bit pointless telling you this but never mind,probably the furthest I've walked is from the far end of Pernera to the far end of Protaras and back.Bearing in mind that Pernera is classed as Protaras it probably isn't that far but in the heat of the day it is a fair trek.I would say the walk from Nissi Bay to the Harbour and beach area of Ayia Napa would be roughly the same distance but you've then got the distance from Napa to Konnos Bay to do which,at a guess is twice that distance again.
If you go to google earth you can get a pretty clear look at the area,Konnos Bay is clearly identified as is Nissi Beach so you'll get a good idea of what the distance will be.

thank you so much. I will have a look on google earth - that's a great idea..

Oh dear - its further out that I thought!! Do the buses run all night in both directions to get back to this hotel? (whether we are out for the evening in Protaras or Ayia Napa)?

I think it's around 11pm when they stop running,someone will confirm this as I never actually used a bus at night.I'm pretty sure that the bus stop is right outside the Grecian Park so you'll not have far to walk.

oh dear 11pm isnt good - we will just be getting started then hahee! Do you know how much it is in a taxi? Do you haggle for a price? And say we are in Ayia Napa for the day if we get on a bus does the same bus go past our hotel and straight through to Protaras? Thanks for your info..