Firstly I am describing the show not the books, it has been too long since I have read them to recall enough details on the specifics of weaponry/technology. I'll stick to Westeros as well, Essos is a whole mess of other things.

It's difficult to place Game of Thrones using weaponry (there is little time spent on tools or technology) due to it being a hodge podge of fantasy tropes, some with very little resemblance to history. There are very few Glaives/voulges/bills as weaponry for the common soldiers and even fewer maces and poleaxes for more professional soldiers. The weapon of choice for every single person regardless of affordability or practicality is the broadsword, of course almost always wielded minus shield or helmet.

Armour is a more useful way to judge time-period. Aesthetically (Apart from season 1 Baratheon armour, which looked like it came straight from 1066) the armour in the show for most characters and soldiers is most similar to armour used in Europe throughout the mid to late 1300s. Being for the most part partial plate over the torso and shoulders supplemented by mail or leather elsewhere. Though several characters have full plate armour that would look more in place in the mid to late 1400s (Brienne and Loras especially).

/u/GeeJo gave a quite thorough response on this a bit back.

Follow up question with spoilers.

There's a scene in the show where Maester can't-remember-his-name-but-he's-well-dodgy is working on the fallen Mountain with something that looks like bodged-up drip equipment. When would knowledge of this place things? I'm vaguely awards that transfusion was a late nineteenth century science but I don't think he's getting a blood transfusion.