Don't know where OP is located, but some UK providers (for example EE) have had plans that allow roaming in Europe and North America without extra charges.

If, on the other hand, it's important to have a US number so that people in the US can call you without incurring international charges, then the news is not so good. Both AT&T and T-Mobile used to have plans for a basic phone with a US number where for a flat $ fee per day you could have unlimited voice and texts (but no data except when connected to a wifi network), only payable on the days you actually used the phone; but those days are gone. Only monthly plans now.