Speaking of Stanford, from what I understand, the Islamic Studies Program is more of an umbrella organization/forum for all Stanford scholars interested in the Islamic world. It's not a degree program. You would have to apply to one of the established departments: History, Political Science, Anthropology, Comparative Literature or Religious Studies, depending on your interests.
The very best deciding where to apply. You have some excellent schools there! I would recommend you to consider less well-known schools in the USA but who may have excellent scholars in Persian Studies (I expect some UC schools, apart from UCLA and Berkeley, may be great at that). In the UK, for Iranian-related things check out Durham, Exeter, Edinburgh, St Andrews, maybe Manchester. U London contains many semi-autonomous schools now, so I guess you're looking at SOAS.