Start with exchanges that completely prohibit US customers in their terms. If an exchange does business with US persons, they are subject to OFAC jurisdiction. I'm not aware of any hosted wallets that prohibit US customers.
There is Omniwallet (a hosted wallet). I'm not sure where it's based but I doubt it matters in this case as it's fully open-source, and you're only asked for an email and a password to create the wallet.
I wouldn't consider that a "hosted" wallet. Omniwallet doesn't control the user's private keys. Transactions are signed client side, same as Blockchain.info's wallet:
https://www.reddit.com/r/omni/comments/32b8o4/does_omniwallet_hold_the_private_keys/cqc9ve3/Freewallet is more what I think of as a hosted wallet.
A hosted crypto wallet is a digital wallet in which your private keys are stored. In exchange, the wallet takes care of the backup and security of your funds.
In comparison to other crypto wallets, a hosted wallet is more similar to regular banking apps — you can always regain access to your assets, even if you have forgotten your password, mnemonic phrase or lost your phone. Other types of wallets do not provide this possibility. In the event that you lose access to your credentials or a device on which the wallet is installed, you will lose your funds.
Freewallet is an example of a hosted wallet. It provides its users with the possibility to restore lost credentials, performs backups and guarantees security of the user’s funds.