This wasn't some spur of the moment thing either on Nick's part as he had long been aware of the fact he would come into possession of the resurrection stone and thus had been planning what to do with it for quite some time. While the stone was quite the useful item in that it let you summon the spirits of the dead there was a catch that made it nearly useless to Nick. See the stone had a limitation in that it could only summon those who were personally known by the person using it.-
The reason this was useless to Nick was that he couldn't summon say the soul of Chronos or Merlin in order to learn from them. That limitation meant that besides torturing himself by summoning the soul of a friend or family member the stone held no value. Besides that Nick was a firm believer that the dead have no place in the land of the living and the description of the torment the souls brought by the stone felt proved it. Even when angry Nick was never one to purposefully torment others in any meaningful way.-
In the hands of someone ancient such as Nicolas Flamel on the other hand the stone was a source of old and forgotten knowledge since the man could summon the souls of people from throughout his long life and copy down their knowledge. Still Nick knew that the stone would only show it's best in the hands of a member of the Peverell bloodline. Speaking of uses Nick was currently analyzing the stone using his realm and was not surprised at what he was discovering. The stone itself was actually just a normal rock like the sort one might pickup from the road.-
The person who made it into what it is currently however was a masterful enchanter as each grain of the stones was positively covered in tiny complex runes that served as a part of the whole. Nick was fairly certain that if he studied the cloak as well in his realm he would discover a similar thing. The hallows weren't created by Hades but it was clear that he had given the three brothers their inspiration and possibly even taught them via his projection. Why he would do something like this was beyond Nick's understanding and would likely only be answered in the future when he met the god in person , assuming he survived that long of course.-
It didn't take long for Dumbledore to find Nick after he left the old man to his thoughts and apparate them back to Hogsmeade without a word. Clearly the man was still caught up in his thoughts as he simply left Nick in the village before apparating away again. Nick merely shrugged at this and chose to treat the day as an unofficial holiday for himself before having letting out Nazgul from the ring realm. The two of them then made their way over to Honeydukes candy shop to check for new or interesting treats.-
The owner of the sweet shop at the moment was Ambrosius Flume and his wife who both didn't ask Nick a single question about why he was there during the week since he spent close to seven galleons on various sweets. He got some chocolate frogs , every flavor beans , lemon drops and even a blood flavored lollipop that was apparently an experimental product of theirs. Nick helpfully tried the scarlet candy while in the store and admitted that minus the sweetness it held it did indeed taste like blood.-
He even added that if they added a touch of cinnamon to the lollipop it might prove fairly popular. Mr. Flume was grateful for the input and wished Nick well as he left the shop still sucking on the sucker for no reason other than he hated wasting food. He offered it to Nazgul but she smelt the bloody smell of it and literally turned her nose up at it. Helpless he could only eat it himself as he stopped by scrivenshaft's to collect some more ink and parchment for Hermione and Daphne who went through the stuff very quickly with their rune practice.-
While he was there he also grabbed another engraving pen since his was also starting to wear down from all the sharpening's it's gotten. After that he moved over to the three broomsticks inn to indulge himself in a bit of butterbeer that was honestly closer to butterscotch soda than any proper alcohol. It was horribly sweet and had a very low alcohol content meaning it was damn near impossible to actually get drunk off it. The owner of the inn Madam Rosmerta questioned Nick on why he was there during the week but Nick explained how he was left here by Dumbledore which plenty of people saw.