As a general rule, you almost have to have an account at a large commercial full service bank to efficiently cash and/or deposit a foreign check. Sometimes you can avoid this by convincing the payer to give you a check in US$ written on a USA bank or if you receive e check while you are in a foreign country, you might be able to go to the bank on which the check is written and request that it be rewritten in US$ on a USA bank, but this will involve fees including fees for foreign currency exchange. You could also ask the foreign bank, in person, to cash it and give you travelers' checks in US$.

IME state banks, savings banks, savings and loan associations, credit unions, etc. will not deal with foreign checks at all, although some might
be able to route them through some big commercial bank with big delays and fees. Most smaller community oriented banks, even if federally chartered, similarly do not process foreign checks or deal with foreign currencies except possibly for ordering some money for travelers from a foreign exchange specialist or for supplying Canadian currency in northern areas. YMMV.

Remember than you must report the import or export of money in excess of $10,000 or foreign equivalent although it is not illegal to bring any amount of money into or out of the USA per see.