Best daytrips from Vienna?

Some trips I have done from Vienna is the baroque monastery in Melk and the Esterhazy palace in Eisenstadt. Both reached by regular train and a short walk from the railway station.
Others will undoubtedly come with more suggestions.

Within Austria, a charming direction is toward Melk and the Danube Valley. Mauthausen Concentration Camp is a bit further in that same direction. In the opposite direction, the city of Bratislava is a short trip by bus, train, or (not very scenic) Danube boat ride. Rick's Vienna/Salzburg/Tirol guidebook has good coverage of these.

Klosterneueburg Monastery , about one hour from central Vienna by U Bahn and bus is magnificent - look here https://en.wikipedia.org/wiki/Klosterneuburg_Monastery

I will get some push back here, but you can do a great 36 hour visit of Budapest. You take a morning train down (2.5 hours). The first day you arrive at lunch time (eat at a café on the river facing Castle Hill, then walk across the Chain Bridge and up the Funicular to the old Castle Hill District. Stay in one of the great river front hotels. Spend the evening on Vaci utca. The next morning use the No 2 tram to go to the Parliament then back to the Great Market Hall. Follow that with a trip on the 47/49 tram to see the Dohany Synagogue and on to Andrassy ut for the Opera House. Finally hop the M1 metro back to very near your hotel, pick up the day bag an board the M2 metro back to the train station after dinner. Sure, there is 1000 times more, but its an excellent couple of days.

The Wachau in general (the area along the Danube between Krems-an-der-Donau and Melk, not just Melk) is a cliche recommendation, but it's a cliche for a reason - it's glorious if you have good weather.

I will get some push back here, but you can do a great 36 hour visit of Budapest.

Right. You can do this in one day easily. If you take the first train in the morning, you will arrive at half past 9am in Budapest. The last train back to Vienna departs at 8:40pm, so have about 11 hours in Budapest.

You get up bright and early, but not too early because you are on vacation; by about 7:45 you want to be on your way to the Wien Hbf Station for the 8:39 train to Budapest. Cost, about 25 euro last time I checked (advance purchase).

You will arrive in Budapest at precisely 11:19 (more or less). In the front of the station, in the center, you will see stairs that go down to the lower level. http://static-v3c.raileurope-world.com/local/cache-vignettes/L760xH507/hungary-budapest_keleti_station-_c_radiokafka_editorial_only-shutterstock_146545598-27b35.jpg Go down. At the bottom on the right there is a help office. Tell them you need a 24 hour Travel Card. http://www.bkk.hu/en/budapest-24-hour-travel-card/ They will help you with love and a smile. This will cost you 1,650 forints or about $6.00. You can pay with a credit card. With this in hand you can get on any form of public transport and ride for free. Just show the card when asked.

So, do just that. Follow the signs to the M2 (RED) Metro Line. The metro line directions are marked based on the last stop in each direction. Follow the M2 Metro signs that say Déli pályaudvar which is the last stop on the M2 after crossing the Danube River. BUT!!! You will get off at Deák Ferenc tér (3rd stop and in something less than 5 minutes) from which you will follow the stairs up until you see the light of day. http://budapest.poznej.com/files/deak_ferenc_ter_1.jpg WELCOME TO BUDAPEST.

Okay, lunch time. You will need a map and the one that comes with your Eyewitness Budapest Top 10 Guidebook (did I mention that?) is perfect to help you find your way around.

From Deak Ferenc ter you will walk a few minutes to Vorosmarty ter. A “ter” is a square, and Vorosmarty ter is a beautiful one. Where the famous Vaci utca pedestrian shopping street ends http://previews.123rf.com/images/maxbaer/maxbaer1210/maxbaer121000001/15485383-The-shopping-area-of-the-Hungarian-capital-Budapest-Vaci-utca--Stock-Photo.jpg and home to the famous Gerbeaud Kávéház http://i1.trekearth.com/photos/83769/gerbeaud.jpg . But save the sweets for later..

Walk the couple hundred feet from Vorsomarty ter to the river embankment and check into your hotel. Did I mention you were staying the night? The Intercontinental I think is perfect for a one night visit. http://budapest.intercontinental.com/en/ Now out to the embankment for lunch. Just pick a place with a view. The place with the orange striped awnings has great Töltött Káposzta.
After lunch it is time to go to Buda. Walk across the Chain Bridge https://c1.staticflickr.com/9/8400/8678102450_fb359857d8_b.jpg and up the Funicular (the only transportation in town that your Travel Card does not work for. Sorry) http://www.budapestagent.com/wp-content/uploads/2014/03/funicularview.jpg . Use your Guidebook to find your way around Castle Hill. My guess, by 5pm you will be back down and heading for Pest. Do what you need to at the hotel, cause you aren’t coming back before dinner.

A little rest, maybe a drink on the embankment, then head for the Gerbeaud Kávéház. WAIT, not so fast. Sweets are for later. Out front of the coffee house is a metro stop. You want the stairs furthest from the front of the coffee house. This is the famous M1 metro line. Oldest on the continent. Ride it to Hősök tere (Hero’s Square). Guide Book Time.

Now you should walk down Andrassy ut (only one direction you can walk, so don’t worry) till you get to the next metro stop (the M1 runs directly under Andrassy ut), now ride it a stop. Then off and walk a stop, then ride a stop. This is the Champs-Élysées of Budapest. http://www.buddhabudapest.com/wp-content/gallery/budapest-downtown/andrassy-ut.jpg (Christmas time)
At whatever pace you have, when it gets close to 7pm you want to end up at the Opera House. Next door is Callas Café where you have reservations for 7pm (did I mention that?) If you are moving too fast, then slow down and do a little shopping on Andrassy ut.

After dinner walk across the street and up the left hand side of the old derelict gorgeous mansion. At the end of the block, take about a 20 foot jog to the right then continue up the narrow old street till it ends (just one block). At the end at the left is the Kadarka Wine Bar where they have a table reserved for you. (I guess I should have mentioned that too).

When bed time calls, walk back to the Opera House and take the M1 back to Vorosmarty ter where your hotel is located.

GOOD MORNING, its day two. Interested???

I have done the train-boat-train day trip to Melk and that was quite enjoyable, and easy. I also did a long day trip to Salzburg by train, just under 3 hours and I arrived by 10, left around 5:30--just enough to get a good feel for the city, explore and see Mozart's gebursthaus and tour Hellbrunn's gardens and interior. Bratislava is on the agenda for my upcoming trip.

I considered doing a day trip to Budapest, but figured I was so close I should just take the train there and spend a few days...and thus an obsession was born. Heading back for 3rd visit in April.

Go Jim!!
I need to make that trip myself . . . :-)

Up the Danube is a classic. Would be at the top of my list.

May will be very green and lovely. If you want to do more, maybe heading for some of the rural areas to enjoy the landscape. And also visit the botanical garden in Vienna (adjacent to the Belvedere).

Maybe Retz, which is a very good wine region and very easy by train from Vienna. (~1 hour). The center is very pretty, too. If you have a car, you can drive to the Hardegg castle, which is in the a national park. That area straddles the Austrian-Czech border and has several Cold War sites (Iron Curtain--you really need a car or be intrepid cyclists to reach these).

Znaim/Znojmo is a lovely town on the Czech side that you can also get to by direct train from Vienna.

'Best' really depends on what you are interested in seeing/doing. But honestly, with a week here, you will probably need to pick one thing. That's not so very much time really.