The major problem with a 1m sea level rise isn't that land which is currently 1m above sea level becomes permanently flooded. The major problem is that land which is 2m or 3m or 4m above sea level becomes flooded way more often.
Local sea levels vary with winds, tides, and perhaps more importantly storms. A smallish rise in sea level might mean that catastrophic storm surge goes from a 500-year event to a 10-year event (numbers pulled out of my nether regions, just meant to illustrate the idea).
For example, much of the damage from Hurricane Sandy was caused by its huge 13ft storm surge. If sea level rises by 1m, then a storm with only 10ft storm surge will match it, which means damage on that level will happen way more frequently, and a repeat of Sandy would be vastly more damaging.
I think what a map like this needs is a setting which shows where the (for example) 100-year flood level is now, and where it moves with the given sea level rise. This is way more complicated, of course, but would do a much better job of showing the real problems.
https://en.wikipedia.org/wiki/Tidal_range
I happen to have visited both extremes (Caribbeans and the Bay of Fundy).
Description: http://blog.firetree.net/2006/05/18/more-about-flood-maps/
(You can get current and historical sea height satellite data from http://sealevel.colorado.edu/)
If you assume the rate of melting is roughly proportional to the temperature, then we are in for an increase in rates.
But there are other things. Nonlinear ice effects - that are not very well included in IPCC projections, could cause a lot more sea level rise sooner. They are hard to predict.
http://phys.org/news/2015-09-eyes-oceansjames-hansen-sea.htm...
It amazed me just how linear historical sea levels have been. Take a look at measured New York sea levels, which have been kept since before the Civil War.
http://tidesandcurrents.noaa.gov/sltrends/sltrends_station.s...
Perhaps best is to watch this long presentation by Eric Rignot from NASA JPL a few times, it's very fascinating and also terrifying.
https://www.youtube.com/watch?v=3p9uRxX95f4
Imagine two kilometers of glacier sitting on bedrock that's 500 meters below sea level. The glacier doesn't touch sea water because there's higher ground between it and the sea, though still below sea level, and also that's blocked by ice. If that blocking ice melts, the warm and salty water can then touch the big glacier that then starts melting and calving icebergs. Or if the glacier is on higher ground, it can start directly sliding towards the sea.
There are multiple glaciers in Greenland and Antarctica that each could contribute one meter to sea level rise, that the scientists are watching. Eric Rignot named the parts between the glacier and the sea Flood Gates.
We haven't observed ice sheet collapses, so it's hard to know how it will play out, how long it will take, one or more centuries. We also can't afford to wait and observe them and only then do something about it.
For fun, you can get sea level rise satellite data for the past 20+ years from http://sealevel.colorado.edu and run your own math. If you just naively run forward the observed rate over the last 22 years, you get 1 meter of rise in 300 years.
You can also see historical tide data for cities here http://tidesandcurrents.noaa.gov/sltrends/sltrends_station.s...
It's important to know that tide data combines sea level information with information on how much the city is sinking. A bedrock city like NYC will give you better data on sea level rise than a city built on mud, like Venice, which is going into the water even if global sea levels were falling instead of rising.
The one meter over 100 years figure is the worst case number in the reports. Of course the bigger number gets the most press.
The last one hundred years have had a .10 to .20 meter rise, depending on who you ask.
Places like Florida are going to be severely hit by rising sea levels because so much of the land is porous. You can't build a dam to stop the sea if it seeps in from underground.