New Years Eve in Vienna and Geting Home to Sofia

1) I'm going to be in Austria at the end of my 2 week trip just in time for New Years Eve and I just wanted to get a sense of how its celebrate in Vienna. I was told from a friend that Vienna is known for its "First Night" Celebration - what does this entail usually? I know that in the U.S., where I am from if you want to go out to celebrate there are expensive cover charges at almost all bars and clubs for New Years. Is it like this in Vienna? Should we be looking into getting tickets for any festivities/parties? And can anyone recommend an affordable hotel near everything?

2) Also, will things (Museums, Tourist sites, Restaurants, Bars, etc) still be open on New Years Day and Jan 2nd?

3) Does anyone know details on the best/cheapest way to get back to Sofia, Bulgaria from Vienna. I've been told an overnight train may be the best option. Is this something I can book in advance and if so - how?

1.) I don't really know what you mean by "first night celebrations", so I can't really comment on it.
Usually you don't need to visit any party, there is a party in the whole city center. There are no special charges in the pubs, afaik. Just go there and see whether you will get any free seat.
2.) Shops and many restaurants will be closed on Jan., 1st. Also some museums etc. will not open. Jan. 2nd is a Saturday, so everything will be open again.
3.) For flights you can check checkfelix.com. Prices start from 112 EUR one way.

Bulgaria Air flies that route direct, but it might be expensive if it's right around the holidays. Might be worth checking at a travel agent, in addition to checking the website listed in #1.
http://www.air.bg/en

The train can be done direct, once a day, however it is a very time consuming trip taking 21 hours.
Schedules at www.bahn.de.

Dave

1) Vienna city center becomes a party zone at new years eve. It's crowded, many tourists, at midnight everybody heads to the Stephansplatz (cathedral square).
(The big bell of the cathedral only rings twice a year on 26th of December and at New year (midnight) it's something special and is broadcast on all radio stations.)
Another tradition is the waltz at midnight.

No idea what you are expecting, but there will definitely be loud music and a lot of alcohol out on the streets, if you prefer to stroll around you don't have to enter a club or a bar, or may be only after midnight.
There are also celebrations in front of the city hall (Rathaus).
It might be wise to book hotel and restaurant in advance.

2) On the 1st the city is rather dead.
But most museums usually open on both days. (But they might close earlier on the 31st open later on the 1st, check on their websites)

New Years Eve is called "Sylvester" in German. That might help, when you are looking for information or special offers.
Never heart about "First Night".

Just waiting now on jman98...