Modern AU: Hipster Solas, Fenris, and Blackwall. 
Huh. Hipster!Solas is kinda doing it for me right now. Even though he appears to nearly get his face smashed by raging hipster!Fenris.
Also, I like Blackwall's man bun. Nice touch.
Mine would consider Cassandra, Dorian, and Cole her friends. Leliana as well, after a time. Dorian I headcanon as her closest friend, and I also imagine Cassandra would ask, though maybe be a little awkward about it,as she is in the banter post-vallaslin removal. Cole taught her some things, since she's Dalish, but it was definitely Solas who opened her mind about spirits and such first, which prepared her for Cole.
The game makes it clear due to the gossip in the hall, as well as comments made by some companions if you talk to them (Sera, Vivienne) that people know about her and Solas, though I do imagine they keep things at least somewhat low key and a bit private for the most part.
My Tala considers Dorian her best friend in the Inquisition, with Cassandra (unexpectedly), Varric (predictably, because who isn't friends with Varric) and Sera (on a hot-cold basis) also becoming her good friends. And Iron Bull becomes a fairly good friend, too. Perhaps mostly because of his relationship with Dorian bringing them closer.
She is fascinated by and protective over Cole, but finds it difficult to have what she considers a normal friendship with him, as she chose to keep him on the spirit path. He feels more like a beloved, disordered child to her. She's on friendly terms with the advisors, getting along best with Josephine, and struggles to trust Morrigan, is lukewarm on Blackwall and doesn't really get along with Vivienne.
Solas is the person she feels the strongest connection with, but it's not just friendship, so. Yeah. I struggle to imagine coming out of playing Inquisition feeling like your Inquisitor was friends with no one, personally. They're a nice bunch.