Check with stock brokers. Some of them will offer ILS->USD conversion at a very beneficial rate (very close to the official), without any commission, and flat-priced wire transfers. For large amounts this is perfect. I know for a fact that Gaon Trade used to do that ($15 for a wire transfer of any amount), but they are now defunct... Check with Meitav (their successor) and others if they still do these things.
If you're talking about relatively small amounts (up to several thousands $$$) - you may be better off withdrawing cash or using your credit card in the US. For mid range (up to $50K give or take, depending on your shopping and bargaining skills) banks may be cheaper.
A quick note about what jamesqf has mentioned in his answer... You probably don't want to tell your banker that you're moving to the US. Some people reported banks freezing their accounts and demanding US tax info to unfreeze, something that you're not required to provide according to the Israeli law. So just don't tell them. In the US you'll need to report your Israeli bank/trading/pension/educational/savings/insurance accounts on FBAR and FATCA forms when you're doing your taxes.