I'm the author of Prince of Thorns, King of Thorns, Emperor of Thorns, & Prince of Fools - spare ideas land here.
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The tower of Joy from GoT (its pretty small)
The Crown Tower from Sullivans Ryria books. I'm not sure how tall it is though.
The Tower on which Pug is tested in Feist's magician.
The Sinspire casino from Red Seas Under Red Skies by Scott Lynch. It would be towards the left, though, since Locke and Jean climbed down the outside of it.
The Tower on Wind Plain from The Riddlemaster trilogy by Patricia McKillip. No idea how tall it really is, as it's hidden by magic and is one of those that you climb and climb and climb and are never to the top until you discover the secret way of getting in.
There's a Tower of Babel in Michael Swanwick's The Dragons of Babel and other books in that world. I have no idea how tall it is, as I don't recall it being mentioned in that book, and that's the only one I've read.
What about Brook's Paranor from the Shannara books?
Not a tower but ice wall in GoT is ridiculously tall isn't it?
700 feet. But I'm wondering just how high up is the Eyrie?
All the sorcerer's towers from the Belgariad, particularly Belgarath's.
The White Tower from Robert Jordan's The Wheel of Time series