"She goes into the kitchen."
Translation:Hun går ind i køkkenet.
Literally, the two mean 'in' and 'out', respectively. What you use depends on the room, I guess.
It sort of depends on how central the room is compared to the room you're already in. For example, I would probably say "ud i køkkenet" if I were in a bedroom or the living room, but I would say "ind i køkkenet" if I were coming from outside, the hallway, the utility room etc.
Bedroom: I would only ever say "ind i soveværelset".
Living room: If I were coming from my bedroom, I might say "ud i stuen". Might. From all other locations, it would be "ind i stuen".
Bathroom: If my focus were on leaving the current room, I would say "ud på badeværelset". If my focus were on going into the bathroom, I would say "ind på badeværelset".
Entrance hall: I would always say "ud i entréen", unless I was coming from the outside.
Utility room: (these are ubiquitous in Danish homes) I would always say "ud i bryggerset"
My recommendation would be to just stick with "ind i/på" since that is never wrong and never sounds strange to Danish ears.