"High spots and fresh air"
 

Wife and I are heading to Prague, Vienna, and Budapest next month, 3 days in each. I like to get a visual overview of each city upon arrival by going to a high place (e.g. Eiffel tower in Paris, radio tower in Berlin). Suggestions for sites in these cities? Also outdoor ideas for the day of arrival in Prague when fighting to stay awake until dusk, at least for me, is best done in the fresh air.

In Vienna you can ride the ferris wheel in the park.

Prague - the tower in Old Town Square. Walk around Prague 1, looking at the wonderful architecture; Charles Bridge. You'll be retiring quite early if you plan to sleep at dusk.

In budapest head to the Castle side of the river and explore the elevated overlooks near the Hilton Hotel.

My favourite spot in Prague is Letna park,if you have seen pictures of the Prague bridges then the photo has most likely been taken from there.
nice outdoor beer garden with great views but go to Hanavsky pavillion for stunning views. it is more expensive to eat and drink in there but worth it in my opinion.
http://hanavsky-pavilon.cz/index.php?jazyk=en

Or you can climb up each of the towers on the Charles Bridge - there's one on the old town side and one on the Mala Strana side.

In Budapest, Fisherman's Bastion or Gellert Hill.

In Vienna, weather permitting, take the 38A bus to the top of Kahlenberg for excellent views of the vineyards and the city. And, for the fresh air.

Also, the Donaturm in the 22nd (off the U1 Alte Donau stop) is the tallest structure in Austria. At the top is an observation deck, cafe, and restaurant.

I love all the towers in PRague, the Powder tower and the towers on the Charles bridge and the St.Vitus cathedral tower. The wind is great and the views are awesome.

For a different perspective on Budapest you can climb to the top of St. Stephen's Basilica, on the opposite bank of the Danube from the castle and Gellert Hill.