Reality - Stark's agreed to keep it in a high security lock-down at the Avengers' upstate Headquarters, outside of the city.
Power - I'm returning this to Star-lord and friends. If they need any additional assistance while on Earth, I suggest that Nick Fury and his agents can offer assistance.
Space - The stone is already bound. Leaving that binding in place between the King and Prince of Asgard is a reasonable solution.
Time - The has long been in the keeping of the Masters of the Mystic Arts and the Sorcerer Supreme. That trend will continue.
Mind - Destroyed. Thank you, Wanda.
Soul - Well out of reach, now that the link volunteered to remove themselves from the equation.