Requested from beany 16 - The Avengers move into the tower after the Battle of Manhattan. Hope this is what you were looking for, and so sorry it took so long for me to get around to finishing it... :(
Well, to begin with, it was Tony and Pepper, living in small corners of the tower whilst the rest of it was repaired after the battle.
Bruce didn't have anywhere to go, he'd spent all of his time hiding away, keeping himself private. Although he was living in a construction site for a few months, he didn't mind. Tony and Pepper, without even asking if they wanted it, had built every member of the team a floor, leaving them as blank slates for them to personalize, once they moved in. To keep him happy, and to make him feel safer, Bruce's floor was reinforced, Tony trusted him to not have an 'incident', but Bruce didn't. Quite often Pepper would wake up in the morning to find them both slumped over in their lab, projections and experiments scattered around them.
Steve arrived soon after, too many mornings spent waking up confused in a strange apartment, too many days spent working out how modern life worked. SHIELD had given him an apartment after the battle, but it was too similar, and too different, to his old home in Brooklyn. It reminded him too much of Bucky, of Peggy, who he could never see again, at least not in the way he remembered them. Peggy was older now, SHIELD had kept an eye on her, but he could just remember missing her date, 70 years of regret now stood between them. He still jumped when JARVIS spoke, and like Thor, had a habit of looking up at the ceiling when speaking to him.
Natasha wandered in after a mission with Steve, and then never left again. She'd never had a proper home, always being moved around between missions for the Red Room, or for SHIELD, living where she was needed at that moment in time. Her floor on the tower was the first place she could call her own, before she had had a semi-regular room in a SHIELD base, but it wasn't personal, it wasn't her own. Sometimes after a mission she would return to find another agent in there, but she knew she wasn't supposed to be attached to things like that. Slowly she began to make the floor her own, turning a small area of it into a ballet studio, to take that memory back from the Red Room, and make it her own again.
No one was exactly sure when Clint moved in. Natasha claimed she knew when he first arrived, and he was living in the vents until she pointed out he had a floor, and may as well use it. He'd been kicked out of another apartment, and left all his items in storage whilst sleeping in the vents in the tower, stealing food from the communal floor at night. Tony was annoyed with JARVIS for not telling him Clint had arrived. When Clint realised the floor was his to do as he wanted and Tony had allowed them, with the discretion of JARVIS, to buy what they wanted using his money, he brought pillows, lots of pillows, creating a large nest in the corner of his living area, which most nights he slept in, unless he was in the vents. He had a habit of using the vents to travel around the tower instead of using the elevator or stairs. He wouldn't admit how many times he had ended up in the wrong floor or room, although he was trying to convince Tony and JARVIS to install maps into the vents, especially after he fell into Natasha's, thankfully empty, bathroom.
Thor was one of the Avengers who actually had a home, but of course he had a floor in the tower too. Situated near the top of the tower, there was a landing pad outside, where when he visited, he would arrive on. Although he didn't stay all the time, whenever he did visit he brought things from home, decorating his floor with ornaments and furniture from Asgard. The rest of the team suspected he took things from Misgard, or Earth, back to his home. Often, Tony would find electronic appliances left on the floor outside his workshop, broken, or not working. He would fix them up, write Thor some simple instructions on how to use them properly, and return them to him.
The whole team made it their mission to acquaint Steve and Thor to modern day Earth, with Movie Nights at least once a week, working through the classics, in a floor Tony had set out with a small cinema room, furnished with comfortable chairs and beanbags. Most nights after a mission, unless they were so tired they just collapsed when they got in the door, they would play games, occasionally getting too carried away. Thor was now banned from pictionary after he got the word 'lightning' and set the chairs on fire. Monopoly was also treated with caution, after Thor landed on Tony's Mayfair with a hotel, and threw the board across the room.
Any new appliances were introduced with a detailed set of instructions, and usually a demonstration. Steve often grasped new concepts pretty quickly, but Thor was the main reason for replacements being needed, especially if Clint taught him how to use the item, usually with incorrect instructions. Thankfully Thor knew how to make poptarts with little fuss, so whenever he was hungry, the team could mostly leave him to it.
Natasha and Pepper soon struck up a friendship, as the only females in the group. They shared the role of 'babysitting' the Avengers, checking Tony occasionally slept, making sure Clint hadn't hoarded all the food in the vents, where he forgot about it and it grew mould. Helping Steve with a new bit of information, or explaining gently to Thor how to work something after Clint had confused him and Tony had given up. Making sure Bruce left the lab sometime, and actually ate something. Sending Clint to take Tony and Bruce some food, when it was obvious to everyone they hadn't left the labs for days, caught up in some experimenting. Pepper waiting when they returned from a mission, watching the landing pad through the window, and rushing out to check for injuries, JARVIS on alert for medical assistance should it be needed.
Steve rediscovered his love for sketching, often sitting in balconies or windowsills, pencilling in a drawing from their latest mission, or a view from the tower. Occasionally he would sketch the others, in the tower, when they were occupied by their hobbies. Natasha practiced her ballet, hidden quietly on her floor, occasionally watched by Steve, once she trusted him to draw her. Clint persuaded Tony to let him get a dog, Lucky, a rescue, and practiced old circus tricks, occasionally going out and performing in orphanages, raising money to help them. Often he would take Lucky along with him. Bruce was a scientist, loving nothing more than to experiment, creating new potential theories, and helping out Tony. Tony had his suits, creating and experimenting with them, as well as creating new things for the tower, gadgets for his team mates. Thor enjoyed going out and exploring the city, usually with one of the Avengers, as he didn't quite have the knack of acting like a Midgardian, and most people noticed him. Pepper ran the Stark company, but spent as much time with the Avengers as she could, often going out with them in an evening, or for shopping during the day.
Together, slowly but surely, the team bonded together, becoming a family, a friendship, a group they never thought would need each other, but certainly slotted together. Although no one ever thought it, they needed each other, the world needs them, and together, they are, the Avengers.