You can absolutely keep them in the same room and let them out of cages for separate runs times - I think this is probably the most common method. Just make sure to put a little distance between the cages so they can't fight. Many people also switch bunnies between cages every couple of days so they can get used to the other bun's scent on toys, litter box, etc. If your bunny is free range all day, you could possibly let her free range one day, then let the other bun free range the next (with a shorter playtime for the bun who has been in a cage all day) - just make sure they aren't going to fight through the cage bars while you're not around, or block the other cage off from the free-ranger bun.

For neutral territory, most of us use bathtubs or bathrooms since the majority of bunnies haven't been there, then expand to other rooms once they are doing well in the bathroom. Some people just set up an xpen in a neutral room of the house. I liked the tub because the sides are low enough for me to easily reach over, plus the slippery floor slows down chasing bunnies and makes them less sure of themselves.

Awesome! Thanks a bunch I'll be adopting in the next few days!