When you arrive in Israel, you will be asked to open a bank account. There are several banks you can choose from. Here we will advise based on our own experience. Usually the bank that has worked better for the Post-docs questioned about it is Discount. There is a branch close to Givat Ram, at Denmark Square (Kikar Denia, in Beit HaKerem).
Usually the banks do not give you a credit card from the beginning, and it turns out it is necessary to have one for many services, like having your own telephone line. When opening the account (ask for a student account), you should be very clear about the need of an international credit card (you may have to make a deposit in the account in order to get it). Be aware that most of the banks in Israel charge an administration fee of ~10 NIS/month.
The banks are generally open from 8:30-12:30 daily except Friday and Saturday, as well as a few afternoons each week (most are open 16:00-17:30 Sundays, Tuesdays and Thursdays). Your bank's schedule will be posted on the branch door. Whether you bank in the morning or afternoon, the banking day ends at 15:00; transactions completed after this hour will be validated as of the following day.
The banks offer online services, but if you want to transfer money internationally, you will have to go to your branch.