Steve:
After getting engaged and deciding that it was time to move in together you decided that you should get a new place for the two of you to live, instead of one of your apartments. You spent a few weeks looking and ended up settling on a beautiful town house in Manhattan, that was bigger than you were both used to.
Bucky:
Since Bucky moving in with you was inspired in part by his need to get away from Tony, he simply moved into your apartment with you. Your apartment was the perfect cozy place for the two of you, and you had a great couch for cuddling. He was happy to be away from Tony, and even happier to be living with you.
Pietro:
Pietro and you ended up moving in together to a new apartment. Your apartment was pretty old and needed constant work, and Pietro had been living at the tower, so you both decided a new place was in order. You moved into a place a couple of blocks away from your old place that was the same size, but much nicer.
Loki:
Loki of course moved into your place with you. You had pretty great apartment, with nice neighbors, an attentive landlord, and a decent rent rate. This meant you had no desire to leave it and Loki thought it was perfect as well, mostly because you were living there though, and less because of the apartment itself.
Clint:
Since your lease being up was the thing that inspired Clint's offer to move in together, you moved in with him. You were nervous at first about invading his space, but he quickly made you feel like the place your home as well. He also made it very obvious that he wanted you there, and told you so.
Thor:
Thor moved in with you to your place. It started with him staying over more and more often, until he was basically there all of the time. Eventually you asked him if he was okay with just calling it official and saying that you were living together. He was of course happy to admit that the two of you shared a living space.
Tony:
Tony renovated an entire floor of the tower to make a new apartment for the two of you. So you could say that you moved in with him since he already lived in the tower, or you could say that you to moved into a new place, since technically your floor of the tower was a new living space for you.
Natasha:
Natasha insisted that you moved in with her. Her place had so many different hiding places for weapons, which made her feel more comfortable. You on the other spent weeks trying to learn where they all were so that you wouldn't accidentally stumble upon the wrong one some day.
Wanda:
You and Wanda decided that since she moving out of the Avengers and since you apartment was pretty small that it would be better to move into a bigger place. You two found a bigger apartment in Manhattan that even had a second bedroom for guests, and your bedroom wasn't the size of a closet, for the first time since college.