The First bank of Mommy and Daddy – after all, they’re the ones that will be financing you 🙂
Seriously, though – find a US bank that allows you to make ATM withdrawals abroad without fees – First Republic, A”H, used to do this, but I think TD or Capital One may also have this; you should check them out. This will enable you to have cash transferred to you in Israel by having someone in the US (rich Shver?) deposit USD and you can then withdraw as NIS.
In Israel, the services are relatively similar – so it will really be more a matter of convenience. Note that as a non-Israeli, you may have restrictions on having your account go negative – so you should check that out.
As to credit cards – I completely agree with the suggestions above on having a US credit card that does not charge foreign fees. This can be the best way of converting funds, and certain features of US cards that are not standard on Israeli ones can be very helpful – though you need to check if there’s a country exclusion for Israel. You should also try to get an Israeli card in Israel (it’s generally the same card as the one you use at an ATM), since certain vendors either don’t take or have issues with non-Israeli cards.
an Israeli Yid