Where does an Oscar winner go when they leave stage after accepting their award?

They go backstage, where they absorb their triumph and are also photographed and congratulated.

Just Google Oscars 2016 backstage and you will see many links. A few pics are of Brie Larson and Alicia Vikander with trophies in their hands and displaying emotions.

http://www.usmagazine.com/celebrity-news/pictures/oscars-2016-candid-backstage-show-moments-w165639

There's a couple of very detailed articles online describing this process, including this one over at Click Online which is well worth reading.

A shorter version of a similar article, hosted on News.Com.Au, also describes the process:

As soon as someone wins an Academy Award, they’re ushered off stage where they’re handed a glass of champagne and they’re given a minute to soak it all in before starting the walk.

And then it begins. They’re taken up the path and escorted out the back of the Dolby theatre to the adjoining Loews hotel.

The first stop is the photo room, where photographers from around the world are gathered to snap pictures of the Oscar winner holding their shiny, 3.8kg trophy.

After a few minutes of posing, they’re then taken next door to the interview room where more than 300 journalists are eagerly waiting to see if their question can be one of the handful that the star will answer.

Armed with numbered paddles, the journalists will raise their arms in the hope they can elicit an answer from the Oscar winner that will make headlines around the world.

After the photos and the questions, the stars are then either escorted back down Winners Walk to their seats in the Dolby Theatre, or, if the show is almost over, they have the option of hanging out in the Architectural Digest green room backstage or they might choose to go directly to the official after party, the Governors Ball.

As mentioned in other answers, it is true that first, the winners are given a glass of champagne and a couple of minutes to calm their excitement. Then they are taken to the hotel next door for a round of photographs (only a couple of minutes) and then the journalists in the room take over and ask questions. As there are a lot of them, only a chosen few get to ask a question.

After the interview part, the winner can head back down Winners Walk to the theatre or, if they want, they can go back into the auditorium to watch the rest of the ceremony (sometimes necessary if you're up for multiple awards) or chill out in the backstage Architectural Digest greenroom.

Once the Oscars are finished, they can go to an after party, the official one being the Governor's Ball. Something quite interesting is that when you receive your Oscar it doesn't even have your name on it, partly to ensure that the winners aren't revealed ahead of time. In the past, winners had to send the beloved statue away to the Academy for the engraving process, which often took several weeks. Now, they can head along to the Governer's Ball and get their details put on a plate while they wait.

Here's Leo being his adorable self (and making self-deprecating jokes) while he is getting his statue engraved.

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