I can give you a few pointers as to where to shack up though not so much on night life as I am more than twice your age.
Vienna is a fairly small city so basically most areas can actually be reached on foot (done it, been there) but there is a very good public transport system too.
Take a look at the map: the downtown/central/first district is not a bad idea to look for a place but probably among the more expensive locations. Same goes for the 7th and 8th which are most trendy right now. Cheaper and also very central are the other "inner districts" (2-9), with the 2nd being maybe the best bet as you are really close to the inner city and well connected in all directions. The 2nd is also a very nice area with lots of infrastructure (markets, all kinds of small shops); it was the old Jewish mainstay and even today has many orthodox fellers in the streets. On the same island as the 2nd is also the 20th which is bound to be a lot cheaper because it is considered further away and grubbier (and maybe it actually is).
The 3rd is a bit off-center but still equipped with subway and other transport connections, it is also very large, so the outer reaches are already "Vorstadt".
4th, 5th and 6th and 9th are nice and close.
Among the outer districts (i.e. beyond Gürtel and Danube), the 13th, 19th and 23rd are the really posh areas, as well as the western parts of the 14th, and 16h to 18th (because they are practically in the Vienna woods and Heurigen areas). Cheap housing mostly used by immigrants and the poor is in the 15th, the inner 16th to 18th, and the inner 10th to 12th. The outer 10th to 12th as well as the 21st and 22nd are the realm of the Austrian proletariat (no entry to council flats without Austrian nationality).
But as I said, PT connections are good, even at night though sparser, and there are no real no-go areas in this fairly safe city. (Though I heard stories of young men being beaten up by gangs around the Millenium Tower several times now, this is a multiplex in the 20th). I guess it mostly depends where you're going to work.
As for looking for a place, there are a lot of realtor websites which you can easily find by googling for
immobilien wien
or by checking one of the local papers online: www.derstandard.at, www.diepresse.at and especially http://kurier.at/immo/ (the "Kurier" used to be, and probably still is, the main paper for housing ads)
viel Glück
Werner