As others have mentioned, you should go into it with the expectation that you probably will move for internship and postdoc. The job market I'd say depends on what you want to do. If you want to go into academia, you probably will move. If you want to set up a PP, well I guess you have a lot of choice in the matter then. If you want to work at a VA or AMC, then you will have to have more flexibility.
All of that said, occasionally it works out how you want to. I fell in love with the city my program was in (and my spouse had a great job in the city), which is a major city, and restricted myself geographically to that city for internship, postdoc, and job searches. I was rolling the dice. It worked out for me - I matched for internship, got one of the few available postdocs, and got an academic job offer, all locally. There was absolutely luck involved, and a ton of stress during the application processes. Had I struck out on any of those searches, it could have altered my career trajectory. So I am not sure I recommend that strategy to the faint of heart. If you are trying to stay in one place, I'd suggest that you a) set yourself apart from your competition, by a longshot (e.g., lots of publishing), b) network like crazy with important local psychologists (e.g., volunteer research assistance beyond what you already do), c) be active in local professional organizations, and d) acknowledge the fact that despite your best efforts, there is a great chance that you'll have to move anyways.
The last thing I'd want is for someone to read my post about an exception and assume that it will work for them too. It is possible, but unlikely to remain in the same place. It might be more likely in smaller cities, but then again, there are fewer opportunities. All of that said, there is nothing stopping anyone from applying for jobs in the city they want to live in, even if you get a job somewhere else first.
