Paphos does indeed have a market located in the old town which is open tuesday to saturday (mornings) and which is well worth a visit.
Apart from the covered market there are also stalls selling local produce and there's a good selection of bars, restaurants and other shops in the immediate area. Prices are considerably better than along the seafront and the tourist area.
I always make a point of stocking up on spices as they're just so cheap - I still have a packet of saffron that I bought a couple of years ago for two euro's - buy it in the UK and you get a few measly strands!
It's easy enough to find if you're driving as the market is well signposted - alternatively you can get a bus from the tourist area as well as from Coral Bay - the number 15.

Have fun

Dave

Hi,

There are several markets in Paphos on different days, I've listed them below & given you a little info about each of them:

Old Town Market - This is open most day of the week, it contains lots of little stores who content is varied & aimed at the tourist, some of the prices are a little OTT (Over The Top) so dont be affraid to barter to get a little discount off them. Most if not all these stalls are run by local Cypriots who're quite friendly. so worth a visit is you like these indoor type of bazzaars.

Duck Pond Market - Is open Wednesdays & Sundays 8am - 2pm. Here you'll find quite a few stalls but it's mainly car booters trying to sell off their own personal stuff, lots of tat, some good bargains but is entirely ex-pat run visited by ex-pats.

Timi Market - is open on Sundays only, 8am - 2pm. This is an open air market located not far from Paphos airport, you'll most likely pass it when you're on your way to your accomadation but you won't see it as it's only open Sunday mornings. It's a mixed market with ex-pats, local Cypriots & anyone else who wants to seel their goods here. you can buy almost anything you like here & imo, it's probably the best of the 3.

There are other markets in Cyprus too, you have the 'Flea Market' at Foussuri just outside of Limassol, near the Akrotiri Base & there's the 'Larnaca open market' which is by far the biggest I've seen on the island, so if you getthe chance, take a trip over to Larnaca & check it out, it's also on a Sunaday morning & takes about 90 mins to get to from Paphos.

Hope that helps

Oh I almost forgot to mention the 'Paphiakos Market' at the Paphiakos animal centre every Saturday, it's just along the roan from the Bagonia Garden centre just up from the harbour at the crossroads... I believe it's now indoors too due to the heat of the summer & all table money goes towards the Paphiakos Animal Charity

The Saturday morning market is the best! Its huge!