My wife and I (both 25) quit our jobs in July because we wanted to move. We travelled for 2 months and then moved to a new city. We were actually able to collect unemployment after waiting for 6 weeks or so.
We have been looking for jobs since September and it's definitely been challenging. We saved up about 25K (after travel), so we have plenty of resources (unemployment helps a lot), but the job market is tough. We both had a few phone interviews, but had to wait until 2 weeks ago for actual in person interviews. Luckily, all you need is one employer to want you and that's what happened to me. Accepted a really good job today.
Quitting our jobs and moving was definely risky, but I think it was the right thing to do because we didn't like the city we lived in. We thought about applying for jobs in the new city before we quit our jobs, but we wanted to travel too. Plus, with our limited work experience (less than 2yrs), it wasn't likely that they would hire us if we weren't available for an in person interview. Why would they, if they can choose from a lot of local options who would be fine for an entry level position. If you are looking for jobs requiring 5+ yrs of experience, it might be a different story.
So, my recommendation is to just move. Maybe try applying for a job in your desired location first, but if you're not getting much response, move. You're still young enough to take this risk. Also, look into unemployment because it can be really helpful.
Btw both my wife and I have a Masters degree, but not in a very high demand field. If I had a science degree or something like accounting, it would've been much easier