I've been city hopping every 3-5 months since late 2021. However my work situation is significantly different than yours, I'm a full-time remote worker, so I've held down the one job all this time and frankly that's made things significantly easier than what you'd be doing. I don't know anything about the restaurant industry, but as someone who has been the hiring manager in a completely different industry, there's a definite risk if you start making a habit of leaving your job after less than a year repeatedly.

When I move from spot to spot I travel by bus, plane, or train - so I travel very light. I've got my 20 liter backpack with my personal and work electronics and a 80 liter sea bag that holds enough casual clothing for ~3 weeks, 3 pairs of shoes, towels, toiletries, a bed pillow, and some other essentials. In all 6 cities I've visited so far I've stayed in furnished rooms/apartments, which generally costs more, but having a furnished place to stay is the key to making this all possible: 3 of the 6 were subleases from college students who either went home for summer or were spending a semester abroad etc, one was an airbnb extended stay, and the other two were craigslist gambles that paid off. I buy the non-essentials that aren't convenient to carry with me from one city to the next and/or aren't provided with the room when I get to the new city e.g. shampoo, bath soap, and detergent.

For the most part I've had a great time doing this, the hardest part for me has been not having friends to hang out with. In two of the six cities I've visited I had at least one friend, coworker, or family member to hang out with, which was great, but in the other four I had nobody. It turns out making new friends in your mid-thirties is really fucking hard. So far my best solution has been that when I need a conversation with a human being, I do the cliché thing and go to a bar because eventually somebody else who needs a conversation will find me. I tried meeting up with three people from reddit at various times, one was very cool so we did a couple days of sight seeing and a hike together, but the other two were definitely not cool, normal, or even sane.