In The Expanse they show New York and also the Statue of Liberty.
I know it's on an island, in the show there is a wall around it.
How high did the water rise? I think it’s more than 15 meters (45 feet), based on this map.
I'm not too sure how high the water has risen in the show, although your estimate looks reasonable. There are some additional shots from the tenth episode in season 2, "Cascade", that give you a look at the ocean and the city, but I couldn't draw any conclusions from it. Take a look yourself.
In the books, we also don't know too much, but we have this description of the city of Baltimore in The Churn:
Sparrow Island stood out in the waves like a widow watching the sea for a ship that would never come home, and Federal Hill scowled back at the city across shallow, filthy water, emperor of its own abandoned land.
Using the (very cool) website you linked to, something around 9 meters looks reasonable. That makes Federal Hill a peninsula, and there are enough small scatterings of Sparrows Point to count as islands. The next level up, 13 meters, makes Sparrows Point all but disappear, but the book does call it an "island" singular, so maybe it is between 13 and 9 meters, closer to 13.
(There might be some more scenes in Nemesis Games that can help pin it down, I don't recall, but there's some other stuff going on in that book that could make the measurement a bit harder.)
At any rate, somewhere around 9 and 13 meters looks about right for the books, which is not too far off from your estimate from the show's opening cinematic.