Euros

You will need some cash for small items. Coffees, public transport tickets, snacks and maybe meals. And as backup in case you have problems with your credit card.
But changing cash US dollars into Euros is an expensive way to do it (and even more so outside Europe). Cheaper to get some Euros from a cash machine (ATM) either at the airport (I assume you are flying in), or as soon as you get into the city.

Standard advice: Always bring two cards, at least one of which is a debit card which works in cash machines (ATM's). That way if one of your cards doesn't work, you loose it, or whatever you still have a backup. If there are two of you each carry a different card so you are not carrying all your eggs in one basket.

What is your "other city" you are moving on to? What currency do you need for that?

Actually two--London and Dublin.

Use a credit card to pay for purchases where CCs are accepted, and ATMs to obtain cash. Using credit cards for cash advices is usually an expensive method and should only be done as a last resort.

In both cases, alert your CC company and bank of your travel plans.

Thank you both for the great advice!

Iwenn,
London (and the rest of the UK) uses pounds (symbol £ banking abbreviation GBP), but the same advice applies. Don't expect to be able to use credit cards for small purchases, get cash from a cash machine (ATM) after you land.
Dublin (and the rest of the Republic of Ireland) uses Euros (symbol €, banking abbreviation EUR). So you can use the spare cash you have left over from Amsterdam.

Read the fine print in your credit card agreement. Forget your fee schedule at home; there often are extra charges for foreign currency transactions. If you are charged $3 per purchase, then using your credit card for everything will quickly get costly. Cash from an ATM with a bank card is usually the cheapest source of foreign exchange, even though it will involve a transaction charge. But using cash for your purchases will spread that fee to the point of insignificance.

Thank you!

As others note, cash (be it EUR or GBP) for the smaller purchases and credit cards for large transactions. My credit union ATM card extracts currency at Interbank plus one percent. My Capital One credit card is basically close to Interbank. There is a lot of forum discussion on optimal (low cost) ways to use ATMs and credit cards.

Keep a supply of coins for public WCs and buses.

As your stay in one currency region draws to a close, manage your cash to minimize the amount of unspent "foreign" currency by paying or not paying with credit cards. If I have an excess of currency pay part of you last hotel using cash and part with credit card having enough cash to get you out of the country.

Great advice!