
nah
near / close
Located at a short spatial or temporal distance.
Die Bushaltestelle ist ganz nah, nur zwei Minuten zu Fuß.
The bus stop is very close, only two minutes on foot.
near / close
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near / close
Located at a short spatial or temporal distance.
Die Bushaltestelle ist ganz nah, nur zwei Minuten zu Fuß.
The bus stop is very close, only two minutes on foot.

close
Having a close personal or emotional relationship with someone.
Obwohl sie weit voneinander entfernt wohnen, stehen sich die beiden Schwestern sehr nah.
Although they live far away from each other, the two sisters are very close.

to affect deeply
To touch or burden someone emotionally in a strong way.
Der Abschied von meinen Freunden ist mir sehr nahe gegangen.
Saying goodbye to my friends affected me deeply.

to strongly recommend
To strongly but politely recommend or suggest something to someone.
Ich möchte Ihnen nahelegen, das Angebot schnell anzunehmen.
I would strongly recommend that you accept the offer quickly.
The comparative forms of 'nah' (near/close) are irregular and are used very frequently: 'näher' (nearer/closer, comparative) and 'am nächsten' (nearest/closest, superlative).
Komm bitte ein bisschen näher.
Please come a little closer.
To express spatial closeness, 'nah' (near/close) is often used with the preposition 'an' and the dative.
Wir wohnen nah an einem großen Park.
We live close to a large park.
To describe a close personal relationship, you use the expression 'jemandem nah sein' (to be close to someone) or 'jemandem nah stehen' (to be close to someone). The person with whom the relationship exists is in the dative.
Er steht seinen Großeltern sehr nah.
He is very close to his grandparents.
The expression 'jemandem nahe gehen' (to affect someone deeply) means to touch someone emotionally. The person who has the feeling is in the dative. The verb 'gehen' is separable here.
Der traurige Film ist mir sehr nahe gegangen.
The sad film affected me deeply.
The expression 'jemandem etwas nahelegen' (to strongly recommend something to someone) is a polite way to recommend something. The person to whom you recommend something is in the dative. The verb 'legen' is separable here.
Ich lege Ihnen nahe, sich gut auf das Gespräch vorzubereiten.
I strongly recommend that you prepare well for the conversation.
next / nearest
Nah only means that the distance is short. Nächst, by contrast, refers to the place or object that is the least distant compared with all the others. So a pharmacy can be near without being the nearest pharmacy.

Eine Apotheke liegt nah, aber eine andere ist noch näher.
One pharmacy is nearby, but another one is even closer.
Die nächste Apotheke liegt direkt gegenüber.
The nearest pharmacy is directly across the street.