It is apparently quite easy to enter Cuba (illegally) as a U.S. citizen, by flying from a third country.
But according to Wikitravel, it can be tricky using a credit card while there:
For Americans, all credit and debit cards from any US financial institution will not work in Cuba. For everyone else, any credit card issued by a foreign bank with a US parent company or US processing firm will also be blocked. In most cases, International VISA- and Mastercard-branded global payment (debit) and credit cards will work, but only if completely unaffiliated with any US subsidiary or US-owned clearinghouse. (emphasis added)
How can I find such a bank, which will allow a U.S. citizen to open an account?
And I should add, if it makes a difference: It should be possible to open an account with such a bank remotely (by Internet ideally, but acceptably by phone, or mail).