Root, roof, room

I pronounce all these words with [u], that is, the same vowel as 'goose', but I've heard some Americans who pronounce the with [U], the vowel in 'foot'. In what areas does this pronunciation occur?

I pronounce all of those words with [u].

I have [u] in all of those words as well.

As luck would have it, this US dialect survey had a question on words like that: http://cfprod01.imt.uwm.edu/Dept/FLL/linguistics/dialect/index.html . And you can look here: http://cfprod01.imt.uwm.edu/Dept/FLL/linguistics/dialect/staticmaps/states.html to see the percentages by state.

What about "hooves"? I pronounce that with [U], but I've heard it pronounce with [u].

Yeah, I do have [U] in "hoof" and "hooves".

Yet in "hoover" I have [u] and haven't heard that with [U].

I myself have [u] in "room" and "hoover", alternate between [u] and [U] but usually use [u] in "root" and "roof", and consistently use [U] in "hoof" and "hooves".

I have [U] in 'hoof' and 'hooves' as well.