One Day in Vienna
 

My husband, teenage daughter and I will have one full day in Vienna. We will be there on a Friday in June. What do you recommend we do to see the most of the city in one day?

you can't see most of the city in one day...

are there any specific kinds of sites you want to see?

If you go to fodors.com and click on the "destinations" tab and then find Vienna, you will get a suggested one day itinerary, with options depending on your interests.

I'd say that the Stephensdom is a must see - it's right in the center of the city and is an absolutely beautiful Gothic cathedral. It has been extensively restored after the war. My next priorities are always to walk up to St. Ruprechtskirche in the old Jewish quarter. It is a romanesque church, a tiny jewel. Then I always have to duck into the Kunsthistorisches Museum, one of the finest art museums in the world. There are other amazing museums as well.

Vienna has many reminders of its imperial past. The Hofburg palace is very popular. The Shönbrunn palace is quite impressive, but I'd rather stay in the center of the city on a one day visit.

Vienna's coffeehouses are famous, and it's fun to stop in one.

I've always traveled to Vienna in the winter, so haven't done the Prater, but I think it would be fun.

The Hofburg complex, in the center of old Vienna, would be a good choice for a half-day visit to its imperial apartments, etc. (Don't know what day it's closed, though).
And, if the Lippizzaners are still in their winter quarters, you could see those gorgeous animals, too, as they are housed at the Hofbug complex. There are 'morning exercises with music' that are good to see, almost as exciting as a full-blown performance if you're a horse lover. The arena where they perform and practice is breathtaking with its domed ceiling, fireplace, plasterwork. You can also tour the stables if you want, which are actually quite humble.
From there, it's an easy walk to the Stephansdom, down a street lined with high-end shops, also many cafes on it and the side streets.
It's quite walkable, especially if you're staying in central Vienna.

We did a day in Vienna in late December in order to show my Son-in-law the city. I was amazed at how much we were able to pack in--and we didn't get there until 10:30 and left at 7 p.m. and it was a driving snowstorm most of the time. You'll probably be able to spend a bit more time and have an easier time of getting around.
This was my plan:
Naschmarkt--one of the best markets in all europe
Walk to Museum quarter and do one of the museums on a blitz
Hofburg Palace and area
Graben area
St. Stephen's
Lunch at Meinl and Co or Nordsee
Walk down Karnerstrasse shopping street to Opera
Take streetcar around the Ring to see Votivekirche, University, Parliamen, Rathaus, Burgtheatre
Get off streetcar at Kartnerring and walk to Karlskirche
Take streetcar to Belvedere Palace to see Klimts
Take streetcar to dinner at Plachutta
Catch train back to Salzburg

Needless to say, that proved a bit too demanding so what we actually did was the following:
Purchased day transport tickets for 5 euros and to S Bahn to Naschmarkt
Wlked to Karlskirche and then to Karlsplatz U Bahn which we took to St. Stephens
Walked Graben and did lunch at Meinl and Co
Walked through Michelsplatz and then to Hofburg
Took Strassenbahn to circle the ring and see all the listed sights,
Got off at the Opera and walked up Kartnerstrasse to St. Stephen's
walked or took U Bahn to Plachutta.

We decided from the get go that we'd have to forego Schoenbronn much as we love it. Would take all or most of a day. Gave up on the museums as taking too much time--but if I were doing it again and had a bit more time, I'd sure try to add the Belvedere back in. It's a twofer--a palace and an art museum and with Klimt paintings that your daughter will see in books for the rest of her life--the Kiss, for instance. You could capture more time by opting for lunch at Nordsee on Kartnerstrasse over Meinl and Co. Nordsee is fast food but the best fast food in the world, IMO.

If you want to read the full account of our time in Vienna, see my trip report entitled New Years in Salzburg. Enjoy Vienna. it's fabulous.

You have some difficult choices to make, which must be adjusted for your personal preferences and objectives.

If you appreciate art, then the Kunsthistorisches Museum is a must.
If you are into the history of the Hapsburg monarchy, then Schönbrunn Palce is fascinating.
If you are into churches, Vienna has plenty of them.
If you are into formerly great estates with gardens that have now been diverted to other use, the Belevedere is attractive.
If you are into military history and empire, then the military museum is good.
If you are classical music fans, then Das Haus der Musik is a good place to visit, although I don't rate it as great, given what the museum has as raw material.

The Bosendorfer piano company at one time had an impressive showroom.

So the list goes on and on.

My suggestion is to get the The Rough Guide to Vienna. Read through it and decide where you want to go.

I don't really think anyone can tell you precisely what to do without knowing your preferences.

For example, I would hardly recommend attending an opera to my brother-in-law, but if there was an antique car exhibition, he would be first in line.
I would do just the reverse for my friend Leonard, particularly if it was a Mozart opera.