Get a cheap and small apartment. Get a job. And honestly just sit on the savings until you have a routine, and a life for yourself where you are earning also. Think of it like a safety net and a "bonus", not a lottery ticket. There's nothing you could do with that money to retire on or anything. It's a lot, but it's not that much these days. Even if someone gave you some smart investment opportunity it could just as easily end up with you having half that money, or none of the money, as it would gaining profit. Maybe use the money for education, or invest it in a secure low-risk fund, something like that. But the key is to get a place to stay, get off the streets, and get that shit in a fund where it isn't liquid. At least most of it. Get a job, get your own life together, and just save that money. Sure, maybe spend a LITTLE of it on yourself. Get yourself a nice place and maybe buy a TV and a laptop or something. But put the rest away.
There will be significant hurdles to easily obtaining a cheap and small apartment. Most want pay stubs, credit checks, previous residence, etc. There is a definite potential problem here if OP truly has the cash, but isn't actually generating income. That can cause him to disqualify for housing like apartments - which sucks, so long as he really has the cash. Why need to show you are bringing in income when you have a nest egg big enough to pay rent for years?
For the relatively sound reason that a bank statement really says nothing about what sort of expenditures the account is responsible for. In fact it basically proves nothing. I had an extra hundred thousand dollars in my bank account just last month, through various circumstances, but it was only nominally mine to spend. Additionally, tenants with jobs have likely already passed through character checks, criminal record checks and so on. Tenants with 100k possibly haven't. A holdover in an extended stay motel is the answer here.Why need to show you are bringing in income when you have a nest egg big enough to pay rent for years?