Great question! The ice caps covering Antarctica are the largest in the world. It has been estimated that if all of the ice covering Antarctica were to melt, sea level would rise by ~60 meters IPCV 2001 report ). Even though this information is from a report that is nearly 15 years old, this estimate probably hasn’t changed much.

You’re right that melting of ice at the North Pole won’t directly affect sea level. That is because the North Pole is covered in sea ice (in the winter). Sea ice and icebergs displace an amount of water equal to their mass, so when they melt there is not change in sea level; the melt water basically just fills the whole that the sea ice or iceberg displaced. Don’t forget the ice cap on Greenland though. Melting of this major Northern Hemisphere ice cap would cause ~7 meters of sea level rise (IPCC 2001 report; see link above).

Keep in mind that there are other causes of sea level rise than the melting of glacial ice. Fluids (liquids and gases) tend to expand when they are heated up, and this is true for seawater as well. The upper layers of the ocean are expanding as the water temperature increases. This “thermal expansion” will contribute significantly to sea level rise as well.

It is more difficult to estimate how much land will be covered if all the ice caps on earth melted. That depends on the topography of coastal areas. A greater area of land will be covered in coastal areas with very shallow topography rising up from the beach. Steeper regions will have less land area inundated (covered by water). Take Santa Barbara for example. Bluffs that are 20–30 meters high in places border much of the coastline. If sea level instantaneously rose 20 meters, not much land area would be inundated. This is a very complicated process though. Sea level rise will probably cause the bluffs to erode back at a higher rate. Also, the “relative sea level” of some regions actually goes down as glaciers melt and the world’s average seal level goes up. This is because the land “bounces back up” after the weight of the glacial ice is removed.

reference:
IPCC 2001 report

The south polar ice cap would result in about 60 meters (200 feet) of sea-level rise. This would cause the flat coasts of many continents to shrink, but more mountainous coasts of continents and almost all inland areas would remain above sea-level.

By the way, it's quite unlikely that the south polar ice cap is going to melt any time soon. It will in the geological future, but by then, the continents will be in different places due to continental drift. Greenland (20 m, or about 70 feet or so) is much more of a worry.

The answer relates to how high the sea level would rise if the polar ice caps melted. The ice caps in the South Pole region would contribute the most to sea level rise if they were to melt. Howevever, there is a lot of ice on Greenland in the North Pole region which would also contribute to sea level rise if melted. Additionally, there are many glaciers on mountain tops-which steadily melt each year-that can also contribute.

If all the Antarctic Ice Sheets (South Pole ice caps) melted, sea level rise would rise about 241 feet. If all the Ice Sheets from Greenland (North Pole region), then about 22 feet of sea level rise would happen. Melting all the mountain glaciers would add only about 1 foot. Melting all these ice sources together would produce about 264 feet of total sea level rise.

However, because ice sheets are very large, a significant amount of isostatic rebound would occur. This means the land underneath some of these ice caps would "rebound upward" (rise in elevation)--like a boat rising higher in water after taking out a heavy load from inside it. Because of the isostatic rebound, the actual sea level rise would only be about 226 feet (if all ice caps and mountain glaciers melted).

If sea level rose 226 feet, it would cover any coastal city that has a mean elevation of 226 feet or less. This would cover many cities on the western coast of California, including Los Angeles, San Francisco, and Santa Barbara. Other U.S. cities, like New York, Boston, and New Orleans, would also be covered (or nearly covered) by water.