Prague Museums and other sight entries.

I didn't try to pay entry fees in euros, which would certainly cost considerably more. It's my impression--from hearing other trourists ask about that in various countries--that it's more likely to be possible at privately owned attractions, which see it as another way to make money. Government-owned spots seem not to want to bother. The situation may be different in Prague.

I saw a fair number of currency-exchange booths in Prague, and the posted rates were often very reasonable, but I don't know what additional fees may be charged. It's possible that it would be less expensive to change some money at one of those booths than to try to spend euros in a country where they are not legal tender. All such booths are not created equal, however. The posted exchange rates can vary.

For an American, using a no-fee credit card at the attraction (if possible) or using a no-fee US ATM card to withdraw koruna would generally be less expensive.

From your phrasing ("does one have to shell out local currency"), you seem to feel it is an imposition to pay in Czech crowns (CZK). It's not. Just go to an ATM and get some, or if a place takes credit card, make sure your card is charged in CZK.

Some places in Prague do accept euros. But:

1) it is never a requirement. Each place (restaurant, museum, etc) can choose whether or not they accept euros.
2) each place is free to set their own exchange rate, which may or may not be close to a fair one.
3) any change you receive will be in CZK.

Unless you are only in town for one day, just get a small amount of CZK from an ATM. You'll definitely need some cash Czech crowns for tram tickets.

Is there some reason you would not obtain and use local currency, especially as it is so easy to do so? Would you accept foreign currency from a traveler in your home town?enter code here

Mucha Museum & Franz Kafka Museum are open every day 10-18, accept euros :)

Try roubles or us dollars and see how you get on.
Here is a tip use euros in Prague in the same way as you would at home