Prague, Budapest and Vienna-8nights 9days

Bus is the cheapest, train is more comfortable. 8 nights for three cities is too hectic. My advice would be skip one.

Thanks for this reply. Which one would you recommend that we go for after Prague? I think we Will go for 2 countries rather than 3. For train, which website I can go to so I can see the schedule so I can buy tickets in advance (if.it will give discount. Thanks in advance

Will go for 2 countries rather than 3
You are not going to 2 countries, you are going to 2 capital cities in 2 countries.
Having said that, I would advise you Prague and Vienna (but others will undoubtedly suggest a combination with Budapest). Both have loads of history and a lot to discover. Best is to get yourself a guide book or to have a look on the internet.
For tickets you can either go to the Austrian railways (http://fahrplan.oebb.at/bin/query.exe/en?) or their Czech counterpart (www.cd.cz/en/)

I always say (so I'll say it here again) that although Prague, Budapest, and Vienna are spoken of as triplets, and obviously have shared history as well as geographic proximity, they are as different as apples, oranges, and bananas. Opinions and reactions to all three vary widely.

I also agree that in 8 nights, you should choose two of them, rather than trying to see all three. Which two? That's up to you. You will only know you've made the right decision when you've seen all three, so that's no help. Read as much about them as you can, and watch videos. Rick's videos are here, and although his Budapest and Vienna videos are getting old, they should give you a flavor of each one: https://www.ricksteves.com/watch-read-listen/video/tv-show

Personally, I preferred Prague and Budapest (again, in very different ways) to Vienna. But then, I seemed to like Vienna less than many others do. Several people in the New York RS travel group were in Vienna last year for extended stays, and had a great time.
A friend of mine loved Prague and Vienna, and didn't like Budapest. My sister loved Prague, didn't care for Budapest because it was so different from Prague (she hadn't had my warning not to expect them to be similar at all), and positively loathed Vienna. You get the picture.

You'll just have to make a return trip to see some of what you missed this time; many of us find travel addictive!

For getting between them, train is usually best, although bus can be cheaper, and a flight between Budapest and Prague may be better than the train for this city combo. To get train schedules, use the Bahn (German Rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules. To actually buy tickets, you'll use the website of the country where the train originates; here's a handy list: http://tinyurl.com/bo8x6o6. To find flights, use Skyscanner: http://www.skyscanner.com/. Be aware that flights within Europe are usually on budget carriers, meaning they charge extra for all kinds of things. Be sure to go to the airline's website and do a dummy booking (up to the point where you put in your credit card) to learn ALL the rules and fees, so you won't have any nasty or expensive surprises. Remember, too, that getting to and from the airports at each end takes more time and money than using the train stations, which are central.

So, 4 nights in Prague is one more night than would interest me. But that's really personal and everyone is different. Now you have four nights left? You really only have time for one place. Your choices are Vienna by train (4 hours and something like $25 to $50 last time I looked) or Budapest by plane (1 hour and about $125 last time I checked). Or I guess you could do 3 or 4 nights in Prague, then use CZ Shuttle or Bean Shuttle to get to Cesky Krumlov, spend a night in this great town, then use the shuttle service to get to Vienna. I think the two shuttle will cost you about $70, but it beats 4 hours on a train and you get to see a great town.

IF, you cut Prague to 3 nights, then I would fly to Budapest, spend 3 nights then train to Vienna for 2 nights. But its sort of a hurried trip.

I would not recommend cut nights from Prague because you will need more nights there going through jet lag.

ija, can you imagine negotiating a 4 year old kid through the crowds of Prague for four and a half days? Eeeeeeee!! Now if I were by myself and I could get drunk with the rest, that would be different.

Crowds in Prague are only in certain places: Old Town Square, Royal Golden Way, Castle. For that I get up early. Everything else is like any other big city. With 4 year old I would go to zoo, or Vltava River, rent a boat, paddle around and feed swans.

Thanks for all the replies.. appreciate it :) learned a lot.. Will do my research on those link shared and buy train tickets :)

In the summer of 2005 when my grandson was 4.5 years old, we took him to Paris and other parts of France, his first trip, went to Eiffel Tower, the Army Museum, Notre Dame, Napoleon's Tomb, Paris sights where kids could splatter in the water due to the heat, and pony riding, etc.

I didn’t do very good at hitting on the children angle. The zoo in Budapest is amazing as is the Circus. The Opera and the Palace of Arts both have children friendly performances. 4 is old enough for the large pool at Széchenyi bath house (get a cabana for the family to use). If the weather is good its hard to beat Maragret Island. Budapest is really a lovely place for children. Here is some more: http://visitbudapest.travel/guide/budapest-with-kids/
http://welovebudapest.com/culture/11.of.the.best.places.to.take.children.in.budapest
http://welovebudapest.com/budapest.and.hungary/have.fun.10.great.activities.for.children.in.budapest
http://travelwithbender.com/travel-blog/hungary/10-things-to-do-with-kids-in-budapest-hungary