I have found that "all banks" do, but not just on the same day. Go to your bank manager and tell her what you want and she should be able to get it. For example only one branch in my city can do it.
I too like to carry a few euros/lbs/ whatever for porter etc. But the best exchange is always the ATM NEVER do it with the little girl at the window in the airport or station. Best is to keep some from previous trip and that way you are always ready to go, In the "old days" Amex had windows in all major cities and they used to give you the bank rate. Unlike darth above, I have never found the exchange offices as good. One other problem which is now fixed for most, European ATMs often require chip cards. Another interesting point is that French banks do not carry cash.