I know I should be less mean about my country's closest ally, but... nah.
Fury made it clear in no uncertain terms that Loki would not involve the Avengers. They would attract too much attention, Thor's apparent betrayal of the Realm would become known and all people would lose hope in their heroes. Loki understood this, understood more that if he were to break his word to Fury his life would become a lot less comfortable very quickly. So no, he did not go to The Avengers.
He went to Pepper Potts instead.
She had been reticent to listen to him at first (she screamed bloody murder and tried to bite him when he appeared in her office) but had calmed down enough to see that Loki wasn't going to kill, maim, incapacitate or harm her in any way and was sat nervously across from him, hands twitching to her coffee and her drawer (where she would be disappointed to see that her pepper spray had temporarily transformed into a signed picture of Loki) as he told her briefly what his mission was.
"So Thor is injured or dead somewhere and you've got to find whatever did it before it kills us all?" She said as she crossed her legs and leaned forward. "And you have no idea what it is yet?"
"I have my suspicions, but I'm keeping them to myself right now. It'd be embarrassing to be wrong, I wouldn't know where to look," he said, watching her closely to see if there was a flicker of a smile. None. "But I have the feeling that even if I find him, we won't be enough to stop this madness by ourselves."
"What makes you think that?"
"Because if this was my plan, that's the first thing I'd make sure I had covered." Pepper frowned, still mistrustful. Loki was impressed by her intelligent instinct.
"Look, I like it here, alright? Not here," he waved to the universe, "Americans are far too loud and what you do to your cheese makes me shiver, but I enjoy your climate and your recreational habits and I've just finished paying my mortgage; I plan to stay and play nicely and that won't happen if everything goes up in smoke." There! The cheese thing, she smiled for a nanosecond. She was warming to him, slowly. "Though it pains me to say this, I need you to get the Avengers ready for action." He sighed, and really hated that what he was about to say was true. "I wouldn't normally see this as an advantage, but the Avengers are quite good at saving the Earth, particularly from people like me." He looked her in the eye, daring her to say something mean. She arched an eyebrow and looked unnervingly like his mother had when she used to try and see if Loki was lying to her.
"You said Earth – I thought we were Midgard to you guys?" she said, Loki completely thrown.
"Well, yes, it's rude to not call someone by their preferred name, isn't it?" She smiled; Loki's charm offensive had worked, as it almost always had done in the past.
"Where do you think Thor is?" She asked.
"Again, these are just suspicions, but there hasn't been any action taken by Asgard yet, so he's somewhere where they can't see him." He thought momentarily about explaining Heimdall's omnispective powers, but decided against it, as he didn't have all afternoon and just thinking about that man stirred up some deeply uncomfortable memories. "There are two places in the entire universe like that, and one of them occupies my immediate surroundings at all times. If I'm right, he's on a miserable rock on the edge of reality, so I'm heading there first." Pepper sat up at her desk and picked up her tablet.
"What do you need me to do?"
Half an hour later, their strategy in place, Loki stood and bowed to Pepper; he nearly took her hand to kiss, but decided it was best not to overdo it. There were manners and there were manners after all.
"Until we meet again, Ms Potts," he said, straightening his back, smiling. She wasn't quite smiling, but it was a close thing.
"So long, Loki. And Loki?" She said as he turned to leave. "I don't know what happened between you and Thor, but he's my friend and... well, just make sure you find him, okay?" He nodded and with a twist, disappeared.
If Pepper was that way inclined, she would have run to the drinks cabinet, but instead went straight to her phone. After the third attempt, her boyfriend finally answered.
"Hey Tony – no I'm not pregnant, why would I – look, shut up for two seconds. You know you said you wanted a movie night with the team, just for everyone to hang out? I think we should plan that. Like, now..."