Austria

You might want to read on available tourism sites at the Austrian National Tourism Office:
http://www.austria.info/ You could start your trip in Vienna and fly open jawed out of another city. A 5-6 day train trip is too long, as the country is just not that large. Travel by rent a car is preferred, as there are so many beautiful mountain lakes to see between Vienna and Salzburg. Then, you could drop down to Innsbruck and see the incredible mountain vistas of Tirol. Travel into Switzerland is not really needed after Tirol--same mountains. You could also see Southern Bavaria, and fly out of Munich's airport. Munich would be a great second large city to visit if you have the time.

Hi Cindy, You could fly into Vienna and spend 2-3 days there and then drive to Salzburg. From there you go into the Czech Repulic and spend 3 days in Prague and go down to Cesky Krumlov (Gorgeous city).

Where in Austria? It may look like a small country on a map, but because the Alps impede travel in several directions, getting from point A to point B is usually slower than you would expect. So, Switzerland is a quick hop across the border from, say, Bregenz, but a much longer trek from Vienna. Late April-early May is the worst time of year to visit the Alps due to the spring melt-off, the frequently overcast skies and rain. Many of the mountain resorts virtually shut down their tourist infrastructure until the summer hiking season starts. If your only reason to visit Switzerland is to see more of the Alps (of which Austria has in spades), this might not represent the best use of your time and money.

I think Austria, specifically Vienna could take up 4 to 5 days, easily. I went there last year for the first time, the last leg of my trip and wished that I had more than 3 days! Then maybe an additional day or two in Salzburg.
Switzerland can provide many day trips, Bern my favorite, Lausanne,Lucerne, Zurich, Zermott and Basel. Then there is the Junfrau. Loved Murren. So much to see in Switzerland, but very, very expensive city. Happy Travels!

Suggest several days in Vienna and Salzburg, perhaps a day or two in Graz, and include time to go beyond the cities (e.g., easy day trip to Eisenstadt or the Neusiedler Sea near Hungary from Vienna; train/boat day trip to Melk Abbey, Durnstein, and Krems from Vienna; from Salzburg, visit the Salzkammergut region or Berchtesgaden in southern Bavaria; explore Styria from Graz, etc.). For the 5-6 days outside of Austria, why not take a 3-day train trip to Budapest and a 3-day train trip to Prague? Again, during the 3 days, consider one day outside of each city (Danube Bend, Lake Balaton, or Pecs in Hungary; Terezin concentration camp or Karlstein castle from Prague). Most importantly, start reading a guidebook now so you can identify places that interest you.

You could also spend the 2 weeks in Austria, which offers far more than just Vienna, Salzburg and the Alps. Vienna is good for a week or more. The city offers so many things people don't know, like the morbid funeral museum, the Hofmobiliendepot (furniture of the imperial court), the Wagenburg at Schönbrunn (carriages used by the imperial household) or the Heeresgeschichtliche Museum (military museum). The Wachau, a valley of the Danube, is lovely in May, and bicycling from Passau/Germany to Vienna is a wonderful experience. And Austria has many great castles and monasteries, like mighty Hochosterwitz: http://en.wikipedia.org/wiki/Hochosterwitz_Castle Kreuzenstein: http://commons.wikimedia.org/wiki/Category:Burg_Kreuzenstein or Rapottenstein:
http://commons.wikimedia.org/wiki/Category:Burg_Rappottenstein I wouldn't visit the Alps in April or early May.

You could easily spend 4-5 days in Vienna. I would also suggest a visit to Salzburg (one of the most beautiful cities in Austria) and then a couple of days in the nearby Salzkammergut (St. Gilgen, St. Wolfgang, Hallstatt). I'd then recommend a couple of days on Lake Constance which borders Austria, Germany and Switzerland. From here, you could easily go into Switzerland for another few days.

Thank you all for your great suggestions. We will we visiting our Son (and our new granddaughter) in Vienna, staying with them for about 3-4 days and then traveling for 1 week. we will return to Vienna to continue our time with our son's family. We are trying to figure out where the best place to go for the week. We will be traveling by train and have only been to Europe once before where we toured Vienna and Munich. Thank you for helping us out with all your wonderful suggestions.

If you get to Vienna and you love it, then stay in Vienna because there is a lot to see that you will also love. BUT!!! If after a day or two you begin wondering why you came, take the first train south to Budapest and finish your vacation there. Worked for us about 10 years ago.