currency exchange on Danube river cruise from Hungary to Prague visiting Austria and Germany

Use an ATM on the ground, either in the airport or the cities themselves, for the best rates. It's really not as big a deal as it seems. Google the Budapest airport, find a layout map, and locate the ATMs - once you're there, just stop at one and withdraw some money (of course, that will only cover you in Hungary). Stay away from Travelex and Bureaus of Exchange unless you are willing to settle for poor exchange rates. There are plenty of ATMs in each country - should not be difficult to access one. Use an ATM card that does not charge you high rates per withdrawal.

Agnes is not steering you wrong. The only real reason to have cash on hand at the airport is if you're going to pay cash for a cab or a bus, but there are a few bank ATMs at the airport which are safe to use. I have always preferred to either rent a car in advance or take the nice Airport Minibus which you can buy a ticket for with a credit card right in the airport. I'm presuming on your cruise they will shuttle you: whenever I see people arriving from the U.S. for cruises they are being met and grouped for some kind of shuttle.

Keep in mind that Budapest is a smaller regional airport. You're going to be tired. You have plenty to worry about like your luggage. You probably won't need cash in hand for anything until you reach your ship. If you want to tip somebody, small U.S. currency or Euros would be fine. If you don't really need the money, just wait until you get settled into your cabin Every restaurant or shop will take VISA and MasterCard.

Those cruise ships are docked right in the center of town and there will be dozens and dozens of perfectly respectable ATMs in walking distance of your boat. They will definitely charge you an exchange fee of around 1%, and there will probably be a withdrawal fee. My credit union remits the withdrawal fee (but not the exchange fee), so it really doesn't make a big difference how often I withdrawal. I developed a preference for OTP (a regional bank) because the rate seemed favorable, and it had a withdrawal limit that I wanted (some banks wouldn't let me withdraw more than $200 a day, but I think OTP was $500.)

The primary reason for you to have cash in your hand once you reach Budapest's streets is to buy kurtoskalacs from a street vendor: https://en.wikipedia.org/wiki/K%C3%BCrt%C5%91skal%C3%A1cs, so make sure you have enough on hand for that.

The same logic applies to Czech Republic and Eurozone countries which you'll transit like Slovakia, Austria and Germany. Just get the currency from an ATM at a regular bank. Avoid those pop-up non-bank machines in airports, bars, etc. because they might be charging extra fees.

Depending on if you are extending your cruise, you will not need large sums of any currency. We like to go to an ATM that is in or outside of a bank. I would get some money in Budapest because even if you are not extending your cruise there will be opportunity for some shopping and the need to tip your guides (unless that is included) And definitely need money for the restrooms. That is why we use the ATM in a bank, so we can get the large bills changed for smaller bills and coins. Since the euro is a great exchange now, we usually bring home euro so I have my purse with euro ready to go for our European trips. And most shops will take Euro (they also need euro for when they go to other countries to shop). Don't forget to call your bank and credit card companies to let them know when and where you'll be traveling.
We did this same river cruise October 2014.. You will love it! PM me if you have any questions. I don't know what company you are using so I may or may not be able to give you info on the company. But the cities you will stop in will be fantastic. Also if you just want just a little money exchanged you may be able to do it right on the ship or get larger bills broken to smaller bills and coins.

Finding an ATM Cash Machine on arrive is your most cost effective option: https://www.ricksteves.com/travel-tips/money/cash-tips

Since you arriving in Budapest, Euros would be as handy as US Dollars in Hungary:
http://www.budapest.com/city_guide/general_information.en.html

Hungary's official currency is the Hungarian Forint (HUF). There are a
number of places which accept Euros too, but the exchange rate
merchants tend to use is significantly lower than what one can get at
a normal exchange office ora bank. The HUF coins' denominations are 5,
10, 20, 50, 100 and 200, while the banknotes are HUF 500, 1000, 2000,
5000, 10000 and 20000.

US Dollars will also be as handy as Euros in the Czech Republic.

Bring at least two ATM cards that are authorized for your travel plans. Same with credit cards. (Only use credit cards for cash in an emergency). See RS tips for added tips.

Agnes is not steering you wrong. The only real reason to have cash on
hand at the airport is if you're going to pay cash for a cab or a bus,
but there are a few bank ATMs at the airport which are safe to use.

The taxi's in Budapest take credit cards. You will get the VISA rate which is the best that there is. Then once you get settled in, ask the front desk directions to the nearest ATM machine. The trip from the Budapest airport to the center of town is cheap by world standards; $25 to $28 with tip and takes 30 to 40 minutes depending on traffic. The Minibus will save you $9 to $12 (for a couple) but the trip could be an extra 30 to 60 minutes depending on the initial wait time, how many drops they have and where you are on the list.

As for what to do with left over forints; PM me and I will give you an address to mail them to.

I'm one who always recommends that someone have some (100 or 200 euro) of local currency in there pocket when they arrive in a foreign country. However, that applies primarily to euro countries. I've consistently found euro at Wells Fargo for an average of 5% over. So if you take along 200 euro, it'll just cost you about $10 for the security of knowing you have cash when you arrive, and compared to a major bank debit card, which takes 3% plus a flat fee which is equivalent to 1%, or 4% total, the cost is minimal (just over $2 for 200 euro).

However, less common currencies, like Czech Koruna, have a much higher rate than euro. In 2012, I paid 14% for Koruna from Wells Fargo. I was going to be staying in a town, Zwiesel, in Germany, close to the border, and my guest card included free use of the trains up to the Czech border. But the ATMs in Zwiesel did not give Koruna, and I couldn't count on an ATM at the border station (there wasn't one), so I paid Wells Fargo $5.60 for 40 Kc, enough for my ticket to Prague. When I got to Prague, I used the ATM at 0% to get more cash.

Lee, its generally good advise. In Budapest in a pinch you can spend Euro just about any place; at lousy rates, but at least you have the option. BUT, if it makes a person more comfortable, then go to the bank and get 40.000 forints for the trip. My bank will charge $152.00 for 40.000 Forints. If you use your Visa card, before any transaction or exchange fees (check with your bank) Visa will charge you $143.00. Actually that's only abut $11 for the peace of mind if you need it; less if your bank charges a lot of fees. Maybe even breakeven. Not bad in my book.