It does seem to be melting quicker and quicker but unless a meteor hits it will probably give inhabited areas time to move.
Short version: There's nowhere ready to move to.
Sure, technically there will be some square acreage to stand on - but someplace to live as people live now? - not so much. It takes a long time to build soil, fill aquifers, adjust ecological niches, grow a forest, etc. There are already seven billion people walking around - the good land is spoken for, in use one way or another.
That said. I think Florida will be with us for some time.
Miami will not - not as the city we know, with a sewer system and indoor plumbing and so forth, anyway.
Yes. He stated there was no liquid water on earth. That is 100% true
You are arguing a timeline - you took, from Nye, the idea that the entire earth was too hot for any liquid water anywhere for "billions" of years. I don't know if Nye actually said that, but it's too simple - as Billvon pointed out by implication, the entire earth average does not have to get below 100C for water to condense out in some places. He posted 300C average as a likely breakover after which some places would cool below 100C. That seems reasonable, and that would likely have happened in hundreds of millions of years - "billions" is less likely. Much less likely.
edit in: overlooked the pressure factor (see below), which means I may have misrepresented Billvon's take. Apologies, if the case. The difference between average and regional temperature on the surface of a cooling planet was the point, not "explaining" billvon, and it stands.