All coordinates on Earth are equally likely to experience a solar eclipse, so it's just a matter of luck where the Moon's shadow happens to fall. But some place has to draw the short straw and be the last in line to experience a total solar eclipse. My question is: where is that place exactly?
The Five Millennium Canon of Solar Eclipses lists all solar eclipses (of any kind) occuring from the years -1999 to +3000. Yes, there's bound to be some inaccuracies, but this is NASA data and you're not particularly gonna get better than that.
Using that data, I'm sure someone smarter than me could gradually highlight all the total eclipses' umbral shadow paths until all but one spot on Earth's surface is covered. Maybe there's a better way to reach the result, but I think I got my point across.
P.S: There is the possibility that even after all the total eclipses from 2000 to 3000, multiple random places would still be uncovered. In which case I think starting from an earlier point would be wise.
Edit: I feel the need to clarify my question a bit. I am not asking about the last solar eclipse that will happen due to the Moon receding from the Earth.
Imagine you had a world map in front of you, and you accurately highlighted the path of totality of every total solar eclipse one by one starting from a certain date. Gradually, almost all the map would be filled as more and more eclipses cover more ground until only a few spots remain. My question is, where are these few unlucky spots that don't get to experience a total solar eclipse?
The starting point doesn't necessarily have to be the beginning of the 21st century. The data I linked covers all eclipses from the years -1999 to +3000. That is 5 millennia worth of eclipses.
After all these millennia have passed, which spots, if any, will remain uncovered on the world map and never experience a total solar eclipse during that time frame?

Here is a combination of the maps available from NASA SEAtlas. They cover time span from year 2001 to 3000. Made with a custom Python script and some editing in GIMP.

The yellow to blue colors mark the time of the next total solar eclipse by location. A red or light blue color marks the areas that do not experience a total eclipse by year 3000.
There are many such areas without eclipse, so based on this data it is not possible to say which will be the last one. There is no clear pattern so it is likely that computational accuracy and the definition of total vs. annular vs. 99% eclipse would affect the answer also.
Here is a map on the number of total eclipses per area in the whole 5000 year dataset:

There are three tiny areas with no eclipses. One is near the border of Brazil and Bolivia, one in north Zimbabwe and one in south Kongo.  I have hilighted them in red.
For some reason the southern hemisphere seems to have less total eclipses on average. An explanation may be in this answer.
