Best way from Vienna airport to friedensbrucke station

"arriving late evening about 11.00 at night"

That late, just take a taxi, that is your best value at that hour.
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https://www.viennaairport.com/en/passengers/arrival__parking/taxis__limousines

Important note: Please only use the taxi rank directly in front of the arrivals hall or the “City Transfer” counter in the arrivals hall. If you are approached in the arrivals hall for taxi service, it is in your best interest not to use it. This is an illegal business conducted by people who in many cases also do not have the required business license.

What would be a reasonable price for the taxi?

It was about 35-40 Euros when I took a taxi into central Vienna, but that was a couple of years ago.
Normally I always take the train because it is almost as quick and much cheaper. I'd have a look at the train schedules and see what time you would arrive at your final destination, if you are up for navigating from there to your apartment after midnight, etc. You know yourself and whether this is something you want to deal with, or if you see the value in getting a taxi and door-to-door service at this time of night.

Thanks for the advice all of you

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.

Thanks wmt1, that was just what I was looking for.

I arrive Friday so the train/tram will be perfect.

The U4 (green line) is a subway line, not a tram.