Size of the Universe at end of recombination (~477000 years)?

The redshift at (re)combination is about $z=1100$. The relationship between scale factor and $z$ is $a = (1+z)^{-1}$. So the universe was about 1/1100 of the size that it is now.

Combining Rob Jeffries answer, Ben Crowell's answer, and adding this tidbit of info:

$$ size ~of~ Observable~ universe~today = sphere~of~diameter~ 93 ~billion~lightyears $$

$$ size~ at~ (re)combination = frac {93 ~billion~lightyears} {1100 ~redshift} ~= sphere~of~diameter ~84~million~lightyears $$

Now, the observable universe after inflation $$(which~ended~at~ t=10^{-23}~seconds)$$ was the size of a grain of sand.

This does not mean that objects moved away from each other at a rate faster than the speed of light after inflation was over.

For a long time this point confused me... I presumed inflation must have lasted for a much longer period of time.

In order to understand how you get from a grain of sand to 84M ly in a time of 377000 years, you have to understand that the space between the events expands such that the distance between them increases faster than the speed of light.

Note that expansion in this sense is completely different than the concept of inflation.