I'm not sure I'd personify Obsidian as only an AA studio, but I get the question.  I remember discussing this with another member on here too.  Three prominent studios that came to mind were all RPG-oriented teams:

-Deck13 (The Surge series)

-Piranha Bytes (Risen series, ELEX)

-Spiders (upcoming GreedFall, The Technomancer)

Now, these devs have made games of varying quality but their concepts and overall design ethos are quite sound.  Bytes and Spiders worst qualities are something a giant, dedicated company can fill: manpower, resources, and technical expertise.  The purchase of all three would probably be the same price as The Initiative built from the ground up.

My most wanted realistic/semi-realistic purchases, other than Obsidian of course:

Sumo Digital- These guys have worked with MS at several points in the past as a 2nd party studio, which already gives MS a potential open door for buying them. They have a talented racing team with Kart experience which could be used to finally make a MS Kart game to enter Microsoft's racing game rotation and give Turn 10 and Playground 3 years per game instead of just 2 years per game. They also have multiple other teams, including the team that is working on Crackdown 3 singleplayer and the team that is working on Dead Island 2. MS would basically be getting 5 AA teams, 3 AAA teams, or a mix of the two such as 2 AAA teams and 2 AA teams depending on how they organized them, which would really help their exclusive output next gen.

Certain Affinity- Founded by former Halo 1 and Halo 2 devs, these guys are top notch, and they've been slowly working on an original IP for years now. So far they haven't found a publisher for the game yet, though a smaller publisher named Leyou invested $10m towards the new IP.

Splash Damage- These guys have been working with MS as a 2nd party studio for the last few years, working on multiplayer for Gears 1 UE and Gears 4. Currently they seem to be working on another Gears game, there were singleplayer job listings for a Gears game at Splash Damage, and they've never worked on Gears singleplayer before. However, buying them is a bit complicated, as they are no longer independent, they were bought by Leyou in 2016, so MS would have to buy them from Leyou, which MS might not be willing to do, though it might be worth it to them rather than having to go through Leyou as a middleman whenever they need Splash Damage to work on a Gears game.

Armature- As you guys know I really liked ReCore, so I'd love to see MS buy Armature, staff them up, and have them make ReCore 2 next gen.

It's definitely looking like you're right about Sumo. They just announced yesterday, after I posted this, that they had acquired another studio, so they are even bigger now than before, over 500 devs now. 

As for Splash Damage, it looks like MS just signed a multi-year 2nd party Gears deal with them rather than buying them and making them 1st party:

“Splash Damage now has a dedicated "Gears of War franchise" team. I expect they have a multi-year deal with Microsoft.”