What you've noticed is generally true of the whole country. Equitably rolling out the vaccinations has been a huge problem we've failed to resolve.
I have been thinking about this and it is hard.
Few weeks ago I heard about a vaccination site in Lowell, poor area of Massachusetts.
Turns out all but a handful who showed up were white and from out of the area.
Tricky thing to do and I think it speaks to poverty and learning.
There is a certain culture of failure or giving up real easily in poor areas. Probably due to:
Education
Upbringing
Being used to being turned away for care due to lack of insurance, lots of paperwork or being shuffled out of the emergency room quickly without being treated much.
Hard thing to address because on the surface we all even my 80 year old parents have internet capable devices, most like my Parents have children to assist them.
Why were the vast majority of slots at that clinic taken by white people? I am going to say they put more effort into scheduling, which is sad that someone would give up or not try because they are so used to losing.
Difficult thing to address, should limited vaccines be sent somewhere they potentially won’t be used? Should vaccines be sent there and just hope people who live close by schedule appointments?
Fortunately it appears there will be plenty for all real soon but it is an interesting discussion.