This... This isn't possible. Not with out a job in the city you want to move to.
I will use New York City as my example city, with out already having a job there, because my sister moved there and had a ton of advice for me when I was thinking about moving out there also. That advice started with having $10,000 saved up because no one will rent an apartment to you if you don't have that much in your bank account.
I'm not joking. Most apartments are $1,800 and up. Mostly up. If you find something for less then that... there is probably a good reason that you will regret.
Location will also effect the price. As will size. Being able to reach the fridge from the toilet is not just a joke but a way of life. You will learn new meanings for the word tiny.
NYC has a whole different kind of renting system then what you will have locally.
Roommates makes sense but it also makes it harder to get a lease. There is a subletting thing were you can rent a room from a person that is renting an apartment... but this is extremely risky. Even if you know there person because you will have no true recourse if it goes bottoms up.
If you have friends or family that will put you up for a month or two then you will have a much better chance to not go broke right away. This is what my sister did until she and her two roommates found an apartment. But they still paid rent.
It can take about three months to find a job if you are in a lucky field of work that is constantly hiring. With the new minimum wage laws you can sort-of live off minimum wage if you share rent. But finding a job can be hard because there are tons of people also job hunting.
NYC has so many people also looking for jobs already there.
This also isn't taking into account that you have to eat and pay for utilities. food is more expensive there. Booze is ridiculously more expensive. Farmers markets are a great solution during the summer and fall seasons. But after that? You have to hunt for good deals. If you have family that visits you you can ask them to pick up staples for you. My mom would bring boxes of instant rice to my sister and other things. She did food shopping like this because a small box of instant rice cost her $6 while large one from home was $2.50.
New York City is a very, very big city. You can not go there thinking people will stop what they are doing to fawn over your new'ness.
A hiring agency will not work with you unless you live in the city.
How will they know? Because they need a current mailing address. This is why friends and family is good to have there because if they let you, you can lie and use their address. Your phone number won't tip them off too much because these days no one changes their cell number when they move to a new city.
I have tried. I even asked if the best way was to live there and was told yes. It's a harsh truth.
This all brings us back to money.
$10,000 is what my sister told me I would need at minimum. That could possibly cover three or four months rent, food and transport with a little for any small emergency. IF YOU HAD FAMILY THERE.
Assuming that you don't have family there... you would want $12,000 - $15,000 or more. Probably more.
This is not possible to do on a shoe string budget.
I hate to break it to you like this, but it took me several years to find out all the ins and outs. With out some kind of support network of good friends and family you can not pull of a huge move. If you had the job first? Then it is much, much easier.
My sister had a job that would allow her to switch to a store in the city. She had family she could stay with until she and her two roommates (one that was a cousin) could find an apartment. I think it took them almost 3 months to find a place and that was only because there were three of them. She was able to do this with less then $10,000 because my cousin HAD $10,000 in her account.
She got lucky.