Web-page view of https://agent.index.cy/api/locations for tools that read pages and follow links. The text below is the complete answer; every address in it is a link you can open. Command-line tools get the raw form.

{
    "results": [
        {
            "kind": "district",
            "use_as": "district=limassol",
            "name": "Limassol"
        },
        {
            "kind": "place",
            "use_as": "location=limassol-agios-athanasios",
            "slug": "limassol-agios-athanasios",
            "name": "Limassol - Agios Athanasios",
            "district": "limassol",
            "lat": 34.71297,
            "lng": 33.05698
        },
        {
            "kind": "district",
            "use_as": "district=paphos",
            "name": "Paphos"
        },
        {
            "kind": "district",
            "use_as": "district=larnaca",
            "name": "Larnaca"
        },
        {
            "kind": "place",
            "use_as": "location=strovolos",
            "slug": "strovolos",
            "name": "Strovolos",
            "district": "nicosia",
            "lat": 35.14046,
            "lng": 33.35032
        },
        {
            "kind": "place",
            "use_as": "location=germasogeia",
            "slug": "germasogeia",
            "name": "Germasogeia",
            "district": "limassol",
            "lat": 34.71232,
            "lng": 33.08172
        },
        {
            "kind": "place",
            "use_as": "location=agios-tychonas",
            "slug": "agios-tychonas",
            "name": "Agios Tychonas",
            "district": "limassol",
            "lat": 34.71914,
            "lng": 33.13199
        },
        {
            "kind": "place",
            "use_as": "location=livadia-larnakas",
            "slug": "livadia-larnakas",
            "name": "Livadia Larnakas",
            "district": "larnaca",
            "lat": 34.95041,
            "lng": 33.63236
        },
        {
            "kind": "place",
            "use_as": "location=mandria",
            "slug": "mandria",
            "name": "Mandria",
            "district": "paphos",
            "lat": 34.75923,
            "lng": 32.62755
        },
        {
            "kind": "place",
            "use_as": "location=aradippou",
            "slug": "aradippou",
            "name": "Aradippou",
            "district": "larnaca",
            "lat": 34.94091,
            "lng": 33.59418
        },
        {
            "kind": "place",
            "use_as": "location=potamos-germasogeias",
            "slug": "potamos-germasogeias",
            "name": "Potamos Germasogeias",
            "district": "limassol",
            "lat": 34.70147,
            "lng": 33.08808
        },
        {
            "kind": "place",
            "use_as": "location=engomi",
            "slug": "engomi",
            "name": "Engomi",
            "district": "nicosia",
            "lat": 35.15789,
            "lng": 33.31794
        },
        {
            "kind": "place",
            "use_as": "location=aglantzia",
            "slug": "aglantzia",
            "name": "Aglantzia",
            "district": "nicosia",
            "lat": 35.15304,
            "lng": 33.39019
        },
        {
            "kind": "place",
            "use_as": "location=geroskipou",
            "slug": "geroskipou",
            "name": "Geroskipou",
            "district": "paphos",
            "lat": 34.75721,
            "lng": 32.45185
        },
        {
            "kind": "place",
            "use_as": "location=limassol-zakaki",
            "slug": "limassol-zakaki",
            "name": "Limassol - Zakaki",
            "district": "limassol",
            "lat": 34.65491,
            "lng": 33.0022
        },
        {
            "kind": "place",
            "use_as": "location=limassol-mesa-geitonia",
            "slug": "limassol-mesa-geitonia",
            "name": "Limassol - Mesa Geitonia",
            "district": "limassol",
            "lat": 34.70022,
            "lng": 33.0483
        },
        {
            "kind": "place",
            "use_as": "location=latsia",
            "slug": "latsia",
            "name": "Latsia",
            "district": "nicosia",
            "lat": 35.10593,
            "lng": 33.38001
        },
        {
            "kind": "place",
            "use_as": "location=ypsonas",
            "slug": "ypsonas",
            "name": "Ypsonas",
            "district": "limassol",
            "lat": 34.69528,
            "lng": 32.95919
        },
        {
            "kind": "district",
            "use_as": "district=nicosia",
            "name": "Nicosia"
        },
        {
            "kind": "place",
            "use_as": "location=chlorakas",
            "slug": "chlorakas",
            "name": "Chlorakas",
            "district": "paphos",
            "lat": 34.79576,
            "lng": 32.40582
        },
        {
            "kind": "place",
            "use_as": "location=limassol-agia-fyla",
            "slug": "limassol-agia-fyla",
            "name": "Limassol - Agia Fyla",
            "district": "limassol",
            "lat": 34.71635,
            "lng": 33.02098
        },
        {
            "kind": "place",
            "use_as": "location=limassol-neapolis",
            "slug": "limassol-neapolis",
            "name": "Limassol - Neapolis",
            "district": "limassol",
            "lat": 34.68843,
            "lng": 33.06265
        },
        {
            "kind": "place",
            "use_as": "location=paralimni",
            "slug": "paralimni",
            "name": "Paralimni",
            "district": "famagusta",
            "lat": 35.03927,
            "lng": 33.99569
        },
        {
            "kind": "place",
            "use_as": "location=oroklini",
            "slug": "oroklini",
            "name": "Oroklini",
            "district": "larnaca",
            "lat": 34.98126,
            "lng": 33.65765
        },
        {
            "kind": "place",
            "use_as": "location=parekklisia",
            "slug": "parekklisia",
            "name": "Parekklisia",
            "district": "limassol",
            "lat": 34.73959,
            "lng": 33.1585
        }
    ],
    "note": "The most popular places first. Pass q=<name> (or several, comma separated) to resolve specific ones."
}