This is the worst choice possible. It was being explored and fished in for as long as we have paper records, and maybe before that. It's not a place you can hide an island bigger than a family car. And because European governments were always keen on grabbing every bit of land they could find and stuffing a flag and some troops on it (it's a habit we got into) you'd be an English/French/Spanish/Dutch/Portuguese colony in no time - if not all of them in turn.
So not the Atlantic. The Pacific was lovely and quiet by comparison (until WW2).
In practical terms the best approach is to hide in plain sight.
Visually hiding it is no good - radar and thermal imaging would spot it. Hiding the civilization underground won't work either - they would have thermal signatures and military surveillance is particularly interested in looking for underground complexes.
You mentioned magic and this does tend to mean they can just magic themselves out of the way, but it's so arbitrary I am ignoring it.
People travel everywhere and mysterious bit of unexplored area tend to attract the curious. The words "no one ever checks that bit" would be like a magnet to geologists, oceanographers, explorers and people trying to get away from everyone else.
Short version: you can't hide so don't.
You hide in plain sight.
You create an apparently poor looking culture, not great climate, no attractive beaches and dull as a very dull thing landscapes. That should keep most people away. Be entirely unhelpful to any visitors.
Stick a bunch of natural obstacles around the island to deter visitors. Nasty jagged rocks just below the sea which are tedious to navigate through, lousy currents prone to drowning the unwary and just be a nuisance enough to deter those determined to be nosy.
Geographically a hilly, rocky place where not much grows but you can graze cattle and live a minimal life (or so it seems). No area large enough to e.g. plonk a runway. No bays ideal for sheltering the fleet. Cliff faces that deter the beach dwelling types and no exciting hills or volcanoes that attract climbers or geologists. Dull, boring, unattractive.
Initially, these things would deter most explorers (although not European monarchies that will colonize places like the Falklands/Malvinas, which are exactly as described :-) ).
Now you can hide the real civilization just behind the scenes.
This part is important: minimize EM radiation - island wide wi-fi is not a good idea to stay hidden. If you set up any comms use carefully hidden wiring.
Likewise, keep thermal emission low or find an excuse for that big thermal hot spot where your generators and industrial equipment are: the island is, after all, allowed to have some industry to keep it going, and it's probably inefficient (or so it appears) and maybe that will do it.
Get rid of any wildlife that could even remotely interest a biologist - those guys are a pain to get rid of.
So people visiting glance at it and go, "bit dull, no beaches, no oil, no minerals, no agriculture worth speaking of, no internet - get me out of here !".
Keep in mind that you mind find that periodically your island is occupied for strategic reasons in times of war. This normally results in the said military leaving when the need of the moment is past and leaving nothing more than a mess behind.
Likewise, by hiding in plain sight, you allow your own people to quite legitimately visit the outside world without raising any real interest beyond "what's Mystery Island like anyway ?", "quiet, dull, poor, no internet" - conversation ends. You can even join the UN and do the normal things: never support any vote or initiative that would draw attention to yourselves.
I'm sure you can do a better job of this idea if you give it a go.
Now I consider magic to be a cop-out, but maybe your islanders can use magic a little to help with this. Whip up a nasty storm that sinks or damages a lot of ships when someone starts parking their fleet around you, that sort of thing ("luckily" the islanders will survive, shaken but in one piece).