I don't want to give names of shops here. Leather goods are sold everywhere on the island.
What To Buy: If you come to Cyprus you will surely buy anything that has to do with leather.
This can be a leather suitcase, (even if it is not leather, the quality is good and much cheaper than anywhere else). Trendy bags, and trendy clothes from the many boutiques in the central area. There are so many shops to choose from. I don't want to advertise one, but each time I fly to Cyprus I see more and more nice shops.
Silverware is also popular and there are many silversmiths' shops. Be aware though and don't trust easily. You might get silver plated things instead of silver.
Some other ideas for Popular Art and Craft Souvenirs which can easily be found across the Island of Cyprus -
Lace Delicate hand-made lace from Lefkara and Omodos has been famous for centuries.
The real hand-made lace is a bit expensive but it is much work and they are worth it.
Rugs and Carpets Colourful decorative and hard-wearing woollen rugs are made in all sizes, in geometric patterns and stripes of red, orange, yellow and brown.
Embroidery - Fine needlework is an age-old Cypriot skill. Embroidered tablecloths, napkins and bed-linen are widely sold.
Icons - Genuine antique fans are rare and costly, but many galleries offer beautifully painted copies of museum pieces.
Ceramics - pretty places- bowls and pitchers in traditional patterns make great gifts, and there are plenty of imaginatively painted modern pieces too.
Gold and Silver - Bracelets, chains, rings and earrings are real bargains. Most gold is 18-carat - look for the hallmark of the Cyprus Goldsmiths Association.
Musical Instruments - Antique lutes, cymbals and drums can be found in many antiques shops.
Reed Baskets - Multicoloured bread baskets are practical and decorative gifts or souvenirs.
Antique Copperware - Look out for old kettles and coffee pots, jugs and antique hubble-bubble pipes in Nicosia.
What To Pay: And if you come to a shop that sells clothes with the metre, especially cashmere check well the quality before you buy.
Don't trust the quality if the trade mark sign is not weaven on the cloth, because there are many owners of these shops that just iron a stamp on the pieces of cloth they sell.
You just have to be a bit careful. You can even ask for a small discount, but don't think that Cyprus is like an Arab country where you can bargain and don't expect the price to go down a lot. Sometimes it depends on the mood of the shopkeeper, but you don't lose anything to ask for a small discount.
Cypriot wine - the iconic local variety known as Commandaria is strong, sweet and somewhat akin to Porto wine
Lacework of an intricate nature - from the village of Lefkara.
Zivania - is a strong spirit based alcoholic drink
Leather goods such as shoes and handbags
Of course after beach and swimming pool we are too tired to go anywhere, but you will save hudreds dollars bying food in supermarket in Paralimni. It is 10 km from Ayia Napa but everything is 2 times cheaper then in the city. We went there to buy water, loukoum for souvenirs all kinds of food and fruits. Everyone knows where Paralimni is and there is a bus comin from the square to supermarket and back. It costs 0.80 CYP
Its enough to visit it twice a week not to pay much more in the city.
Speaking about souvenirs...It's also cheaper in Paralimni but speaking bout Napa - no matter where you go, the price is the same. And almost all shops have the same collection of souvenirs.
A lot of souvenir shops are on Nissi ave and st. Makariou ave.
What to buy: Loukoum, olive oil, saint pictures, towels and ashtrays, wine, honey, olive soap, cups, all sorts of national alcohol beverages
What to pay: I spent 500$ for 2 weeks.=)For food, drink, souvenirs etc.
You can find supermarkets in every corner in Ayia Napa, there you can find everything from food and drinks to souvenirs, clothes, beach things, toys ect ect.