"The site is nearby."
Translation:De locatie is dichtbij.
They are essentially the same, but vlakbij is a little closer than dichtbij, if you want to be specific. Vlakbij comes from vlak which means "flat" or "plane" - meaning on the same plane. Dichtbij comes from dicht which means thick, tight, dense or close. They are interchangeable but if you want to compare one to another, vlakbij is closer in Dutch.
I translated the site as 'de plek' Duolingo says no it should be 'de site'. I don't think that's a Dutch word.
The word 'site' is only used in dutch as a shorthand for a website. 'Plek' or 'plaats' is the best translation for 'site'.
De locatie ligt dichtbij, yes. Ligt is generally for buildings/objects which are wider than they are tall, though, so it may not be appropriate in all situations. If it is taller than it is wide then you could use "staat" instead of "is" in this sentence.