Visiting Neuschwanstein Castle

I think you will find that the fastest route, although not the most scenic, will be through Salzburg and Munich (6½+ hours), and that can all be done with public transportation (trains). One days travel each way and one day in Füssen will be more than enough time. But that is a lot of time spent just seeing Neuschwanstein. If you spend two nights in Füssen, you'll have enough time to see both castles (Neuschwanstein and Hohenschwangau and the town of Füssen.

You do realise that Neuschwanstein is in Germany? That isn't a problem because there is no real border and the money is the same.
The easiest way is train Vienna- Munich - direct at 30 minutes past even hours from Vienna Main station (Hauptbahnhof) takes 4 hours. At Munich you need to change to a regional train, usually to Kaufbeuren where you change to a local train to Füssen. Overall journey is about 6½ hours. It should be possible to buy a through ticket.

It is possible to get there from Innsbruck but it involves a combination of local trains and buses and takes around 4 hours, and that assumes that the mountain roads are clear of snow.

You are investing a huge amount of time to get to a place that is somewhat underwhelming when you are actually there. Make sure that this is worth the effort to you.

I will be in Vienna the first week of December. I would like to see the Neuschwanstein Castle. I was hoping to take a train to Innsbruck

Innsbruck is the wrong place to go to. Look at a map. There are no border controls between Austria and Germany, but there is a big range of mountains (the Alps!).From Vienna you need to go Vienna - Salzburg - Munich, and then south to Füssen.

But, this is really too far for a day trip.:

Wien Hbf depart 07:30, Salzburg Hbf arrive 09:52
Salzburg Hbf depart 10:00, München Hbf arrive 11:41
München Hbf depart 11:52, Füssen arrive 13:58

By the time you get there it is 2pm, no time to visit the castle and get back to Vienna the same day!
There are plenty of other places to see nearer to Vienna

Thanks to all...these posts are extremely helpful. I thought visiting the castle would provide me with excellent views of the mountains. Any suggestions on other destinations?

which mountains? Vienna is in the flat part of Austria. The real mountains are some distance away.

And the "3 days" - is this the time for the excursion or the whole time in Austria?

We will be in Vienna for an entire week. My husband has a conference to attend. We thought we would arrive a few days early and be able to take a train or rent a car to see some beautiful mountains, lakes and interesting landscape. I thought train travel would be an interesting way to see the countryside. I'm open to any suggestions you may have on places to go. Thanks.

Clare, the Alps stretch all the way through Austria. There are places a lot closer to Vienna you could go to.

Chris, I appreciate your help. Any suggestion for an interesting side trip from Vienna that would give us mountain views? I get overwhelmed by reading the tour books.

This is much simpler than the original question.

Go by train to Salzburg, you can do this direct from Vienna airport if missing the first night in Vienna would help the plan. Either stay a night in Salzburg (and catch up next day) or get the Postbus Line 150 from outside the station to a resort such as St Gilgen http://wolfgangsee.salzkammergut.at/en/region-towns/villages/sankt-gilgen/austria/city/430001365/st-gilgen-am-wolfgangsee.html . (usually twice per hour)

I'd do the latter BUT it will be dark by 4PM so if you leave Salzburg later than 14:30 you will miss some of the views.

Stay 2 nights (or 1 if also staying in Salzburg). You want mountain scenery, you've got it here!

Return to Vienna, take the same bus line for the rest of it's journey to Bad Ischl (about 40 minutes in the bus) and get back on the train here. Option 1 is simplest, go north to Attnang-Puchheim and change for fast train to Vienna. The trains run roughly hourly and it takes 3¼-3½ hours from Bad Ischl.
Option 2 has even more mountains. For this you need the 10:10 bus from St. Gilgen to Bad Ischl, then get the southbound train at 11:03 . Change at Stainach-Irdning and Leoben, arrive Vienna Main station at 15:35.

Thank you. Very helpful.