Accept a PhD offer from a local school while applying to others?
There is a general rule that if you apply to multiple academic programs in the same year, then once you accept an offer of admission to one of them, you must immediately contact all the others to withdraw your application, so that they can offer admission to someone else.

So if you accept the offer to join your PhD program at the local school, that is a final decision for at least a year, and you have to withdraw your applications from the prestigious places.  You cannot wait and see if a more prestigious school accepts you.  That would be considered unethical.

If after a year, you decide that you want to think about transferring, you can apply to a more prestigious program then.  However, at that time, your new application will need to include your achievements during that extra year, and the program will evaluate your expectations based on what they would expect a first-year PhD student to achieve.  So depending on how that year goes, your application could become either stronger or weaker.