If one of the reasons you like the summer is the fact that it is also the “kleftiko” season, join the club. I like kebab, I like “mezedes”, but “kleftiko” is a different kind of ritual. Gourmet restaurants even add it in their tasting menus as their main dish and charge 20€ for a mini piece. You don’t need a fancy restaurant or a massive kitchen, but only a “fourni” (built oven) and good quality lamb or goat. This is also why some of the best “kleftiko” makers are butchers that built a “fourni” outside their butcher shop and offer it in their backyard, rather than having a proper restaurant. The more humble it is, the better it is!
The list is not exhaustive and it is mostly for places that, either offer only “kleftiko”, or it is their main speciality. There are lots of other tavernas that offer it as well as part of their “meze” but are not specialized in it (like Aigeo, Stoa tou Dimitri and some more). Originally the research was going to be for all of Cyprus 
but I realized I would have finished it next year (if I survive the high cholesterole levels). At the moment the list is mostly for Nicosia and its surroundings with a few exceptions. If you know a place that it is really worth trying and is not on the list feel free to comment below.
Kyriakos Pallouriotissa: all time classic and open only in the summer as their tables are outside. Definitely one of the best, either for take-away or eat-in on the lovely patio. Highly recommend it!
22432750 & 99630389, Vernardaki 6, Pallouriotissa
Mon-Sat, until end of September
Kakos Aglantzia: very good “kleftiko” with one of the best potatoes: soft, mushy and dipped in the lamb jus. It is best for take-away.
Ammochostos ave (towards SOPAZ),Aglantzia, 22332096
Mon-Sun (+ lunch), until end of September
Pissas Agios Dometios: The only one who offers “kleftiko” all year around, every day except Monday. He also serves souvlakia and other grilled meat for take-away or eat-in. The atmosphere is quite basic as he is on a busy street but his “kleftiko” was very good, with extra special potatoes. It is best for take-away.
Gr. Afxentiou 167, Agios Dometios, 22773378
Tue-Sun (serves “kleftiko” all year around)
Porfyrios Peristerona: no words to describe the Porfyrios experience. Andros and his brothers are actually butchers who started serving one of the few “sirto kleftiko”* casually a few years ago. He didn’t have plates or salad bowls, but only cutlery,
tomatoes, cucumber and onion on each table. In order to get your drinks you had to get up and get them yourself. 7 years later it is very similar, with excellent meat, still served very casually in the paper on the center of the table with tasty tomatoes and cucumber. The only thing that has changed is that they now have plates! Make sure to reserve beforehand. It is best to eat at the restaurant.
centre of Peristerona village, 22823555
Tue & Thu, until mid October
Prosfygas Aglantzia: it seems that Aglantzia area has a large concentration of “kleftiko” makers. Prosfygas is very famous for his “kleftiko” as he has very good meat. There are a lot of tables outside (a bit too many) and it is best for take-away or eat there.
Ammochostos ave 12 (towards SOPAZ), Aglantzia, 22334891
Mon-Sat, Sun until 17:00, until November
Kipos Agios Dometios: the best garden in Nicosia! Relatively new place offering “sirto”* that also serves “pourgouri” and Cretan salad (“ntakos”). I
t is a bit more “refined” (relative to other kleftiko restaurants), which is good if you want to enjoy a couple of more other dishes. He also does limited take-away orders so it is better if you eat there.
Hadjigeorgaki st, Agios Dometios, 22103831
Tue-Fri
Melissos Agios Dometios: brother of the famous Melissos at Mammari village also offering “sirto”* in central Nicosia (together with Klatsimpampas, Porfyrios and Kipos). Fantastic meat, especially if you request one of the best pieces.
Agiou Pavlou ave, Agios Pavlos, 22773674
Mon-Sun, until end of September
Klatsimpampas Tseri: another “sirto”* in Nicosia area (one of the four), and one of the most famous ones! It is definitely worth the drive to Tseri, not only for the fantastic food, but for the beautiful garden as well. Definitely one of the best! Call beforehand for a table, or even to reserve “kleftiko” portions as they run out quite early. It is better to eat there.
Tseri, 22371852
Tue & Fri until mid September
Costaris Derynia village: even though it is in Famagusta district it is so good I had to mention it. 
In Derynia village with a massive garden, it offers a selection of “taverna” food, as well as excellent “kleftiko”. You can tell how popular it is from the amount of people it attracts every night. It is best to eat there.
Derynia village (right as you leave the village), 23822046
Mon-Sun, until end of October
Tamplios Athienou: another one that is not in Nicosia district but I had to include. Enjoying their “kleftiko” under the vine tree in their lovely garden is an experience you have to live.
Athienou, 24522326
Mon-Sun, until September
Note: all the portions were between 6-7.50€ for take-away, and slightly more expensive (in most cases) to eat at the restaurant. The days which they serve “kleftiko” is what the restaurant has set for this year, but their end of season depends highly on the weather
* Kleftiko is slow cooked lamb or goat in a built oven (“fourni”), with potatoes. It takes around 12 hours to cook, hence the limited portions. The reason it is so good is that the meat becomes very tender and soft, while the potatoes absorb the jus from the meat and are the best ones you will ever have. “Sirto” is a way to cook the meat, and it is when, instead of keeping the meat in a pan in the built oven, they put it in paper so that the fat runs out. They say this makes the meat taste better as it is not full of fat and jus, but more tender and pure. It is cooked on ceramic stone.
