It is no problem (and not dangerous) to use public transport during late night hours in Vienna.
You can take the S7 train from the airport (at 11:19pm or 11:49pm) to Wien-Mitte/Landstraße station (a 23 minutes ride) and change there to U4 subway (green line) to go directly to Friedensbrücke station (a 6 minutes ride). The price is €4.30 per person for the whole ride.
(Do not use the CAT train - it is a rip-off.)
If you miss the 11:49pm train, then you must take a taxi, unless you arrive on a Friday or Saturday, when the U4 runs all night, so you may depart from the airport at 12:19am or 12:49am at the latest.