Right Now San is at Citadel and he found the cure of Greyscale there, it is definitely more for Sam to discover at the Citadel. Old Town was founded by the First Men, after all. Throughout the history of the world, they had a lot of secrets, and Sam has already started to uncover them.
Here are 4 things Sam could discover next at the Citadel:
Jon Snow’s Heritage
This one is a bit of a long shot because it is an undocumented secret. However, it is possible Sam will find some detail about Targaryen blood or a small detail about Rhaegar that would point to the possibility of Jon Snow’s heritage.
If Sam discovers that Jon Snow is a Targaryen (capable of riding a dragon), he will contribute yet again to the triumph of man over White Walkers. The more dragon riders, the better.
The White Walkers’ true purpose
In Season 6, we got a glimpse into the history of the White Walkers and realized they might not be exactly what they seem. Sam could discover their true purpose or something crucial about what drives them to march on the world of men after so many years. Sam did tell the Archmaester, after all, that he was there to research the White Walkers.
This could hold the key to either containing or defeating them.
How to forge Valyrian steel
It has long been speculated that Sam will discover the lost art of forging Valyrian steel. This expectation made his discovery of dragon glass a bit unexpected and even more exciting for some fans. However, the quantity of dragon glass is limited.
This falls more into the category of “old magic”, which Sam set out to the Citadel to discover. It is very likely to be hidden away in some old book.
Inspiration to being writing ‘The Song of Ice and Fire’
Okay, so, this is not as much of a discovery as a fun theory about Sam. Many fans think that, after his discussion with the Archmaester about poetic titles, he is writing or narrating the entire series.
If Sam continues uncovering long lost, important aspects of history, it is likely he will start writing it all down. This could lead naturally into a recording of the entire story.