It's not really true across the board that private universities offer more for postgrads (or undergrads) though the top universities and a select few well endowed small colleges offer to meet 100% of demonstrated financial need for undergrads.
In both cases the circumstances of the student are taken into account. DS got a free ride to the local state flagship U for undergrad. This included free transport on the local buses serving the campus and surrounding urban area, which all students got. DD1 got a 95% of total cost financial aid package to the local top 10 in world rankings U. She managed to pay off her loans before graduating thanks to a punishing regime of PT work plus study/classes but she was well set up at graduation. (I think US students do work harder).
In part, the financial package depends on the subject area too - DS' state U pays top dollar for engineering talent across all engineering fields. Not so much for English Lit.
There may be a Tenant Union office in the surrounding area serving grad students (and others) who may or may not be familiar with private leasing, tenant rights, etc. The Tenant Union office was an invaluable resource to a cousin of mine who woke up one day from a nap in her sitting room to find a rat sitting on the arm of the couch looking at her. She terminated her lease and found another apartment with their help.
Some universities offer a list of private certified housing for postgrads and undergrads. This might be worth looking into.
You and DS should really find and then thoroughly mine the resources of the university where housing is concerned.
Your DS should get an Amex card and establish some purchase and payment cycles before heading off. His Amex credit record will follow him to the US.
It's a really good idea to attend international student or PG orientation day, where banks often have a booth offering account starting services, giving out brochures, etc. It's usually considered important to choose a bank with ATMs on campus or close to where the student lives. Since accommodation may not be settled immediately, having a convenient campus ATM might well be a sensible deciding factor since fees often apply for using an ATM not owned by your bank. The vast majority of US banks offer free banking for students. A student would open a checking account (current account) with the option of opening a savings account.
If your DS will have a job (as a TA or some other job on campus) he will have a paycheque, which can either be directly deposited or manually deposited. Without a bank account there may be fees associated with cheque cashing, or outright refusal to cash cheques. He could go to a Western Union desk but fees apply, and it is not a good idea to leave a premises with a few hundred dollars in your pocket on a regular, predictable basis.
It's very important to buy overdraft protection with a US bank account. There is no such thing as running an overdraft in the US. If you go even ten cents into the red you can be charged a whoppingly disproportionate fee plus the amount of the overdraft in order to get back into good standing. A 3c overdraft once cost my DD2 $47.03. Most accounts offer a feature where they freeze an account when the balance dips to a certain level (eg. $50).
There are also credit unions.
It would be a very good ides for your DS to learn to drive in the US no matter where he studies, depending on the terms of his visa www.usnews.com/education/blogs/international-student-counsel/2015/01/06/follow-these-steps-to-obtain-a-us-drivers-license.
Ability to drive is assumed almost all over the world and he will be looking for a job at some point. He will also need some form of state issued ID, and a driver's licence fits the bill. (A state ID would also do, however).
He will need paperwork from the university as well as documentation about his visa to obtain either of these IDs. He needs to contact the international student or international post grad office of his university for assistance and he also needs to look at the state DMV website for his state. He may need a social security number to apply for a licence or state ID. This will require application to the social security administration offices.
Passing the driving test is easy - the difficult part is finding a car to practice and take the test in.
It might be easier to learn as fast as possible in the UK, apply for a learner's permit in the US with all the necessary paperwork, study and take the written exam, then cross his fingers and take the road test before he gets too rusty.