I'm Australian, I understand how the affiliate stations work but can you explain what you mean when you say you don't like your local station?
I'm assuming it's the same as wanting to listen to ABC Melbourne when you live in Sydney - but that means missing out on the local news or particular presenters.
In addition to the other comment, there's simply a huge amount of format variation between local affiliates. Some are mostly music, often classical or jazz, with nothing else except daily news. Others are almost all in-depth news and programming like quiz shows and interview channels.
So there are places where the local station carries almost no NPR content.
Public radio stations across the US carry different programs.
After asking the question I thought about it more and I think I just need to fully commit to podcasts. I've pretty much stopped watching live TV (except for sports) and the same should probably be true for radio.
I'm assuming it's the same as wanting to listen to ABC Melbourne when you live in Sydney - but that means missing out on the local news or particular presenters.