nahegelegen
nearby
Located at a short distance; situated nearby.
Wir gingen in ein nahegelegenes Café, um uns aufzuwärmen.
We went to a nearby café to warm up.

nearby
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nearby
Located at a short distance; situated nearby.
Wir gingen in ein nahegelegenes Café, um uns aufzuwärmen.
We went to a nearby café to warm up.

The word is made up of 'nahe' (near) and 'gelegen' (past participle of 'liegen' (to lie/be located)). So it literally means 'something that is located nearby.'
Wir suchen ein nahegelegenes Hotel für eine Nacht.
We are looking for a nearby hotel for one night.
'Nahegelegen' (nearby) is used almost exclusively as an adjective before a noun (attributively). Predicative use, e.g. 'Das Restaurant ist nahegelegen.' (The restaurant is nearby.), is very unusual.
Der nahegelegene Supermarkt hat bis 22 Uhr geöffnet.
The nearby supermarket is open until 10 p.m.
The adjective is often combined with places that people are looking for or want to visit. Typical examples are 'ein nahegelegenes Restaurant' (a nearby restaurant), 'der nahegelegene Bahnhof' (the nearby train station), or 'ein nahegelegener Park' (a nearby park).
Gibt es hier einen nahegelegenen Spielplatz für die Kinder?
Is there a nearby playground here for the children?
near / close
'nah' and 'nahegelegen' both describe that something is nearby. 'nah' is more general: it can be used spatially or temporally, for example a nearby place or an upcoming appointment. 'nahegelegen' is used mainly for places or buildings that are not far away. It sounds more concrete and usually describes the location of something. In everyday speech, people often simply say 'nah'. 'nahegelegen' works well when describing a place more precisely, for example 'ein nahegelegenes Geschäft' (a nearby shop).

Nach dem Kurs kaufen wir im nahegelegenen Supermarkt ein.
After the course, we do our shopping at the nearby supermarket.
Meine neue Wohnung ist nah am Bahnhof.
My new apartment is close to the train station.