Not only do you need to worry about sound from outside your studio, but depending on your gear, you need to worry about the noise your equipment makes. Since our studio is a converted bedroom, we had a closet which we could easily isolate and convert into an equipment "room"-- but then heat management became an important issue. Run 3 computers in a small sealed closet and they will crash within a few hours.
Since we were doing a gut renovation we were able to put in central air, but it could not be regular AC. The air handler was placed as far away from the studio as possible, and the ducts were over-sized and had a few extra bends. The same amount of air circulates, but the since it flows more slowly we don't hear the rushing air. One vent leads to the studio, the other into the equipment closet. Another difference with regular AC is the return air. Since our room is completely sealed we had to included vents to let the air out, rather than relying on cracks around the door. Doing this with a thin aluminum flexible tube would have punched a great big hole in our soundproofing, so we used 50 feet of insulated tube instead, twisting it and turning it as much as possible: air escapes, but sound can't make it through.
There is another solution if you're not able to put in central air: a ductless system like this one
is fairly quiet and relatively easy to slip in wherever you need it. You just need to have access to outdoor space for the compressor.
Don't forget to plan for power! Use dedicated lines if it's at all possible. Plan where your equipment will be and figure out how much power it will draw. Heat and power are not areas for cutting corners. While your walls are open, think of other wires too. A wireless computer network will not work well in your studio if you build it properly, so it's a good idea to put in some cat6 cables. We have a piano in the living room we knew we would be recording, so we ran a couple digital sound cables from the equipment closet to a closet next to the piano. It's great to be able to make recordings without snaking mic cables all over the place for everyone to trip over.
Another thing to think about is lighting: I don't trust fluoresents because some of them buzz, and I've been trying to eliminate all incandescent lighting (plus incandescent is hot, and there's enough heat generating equipment in a studio as it is....) The obvious answer is LED. This light
can be surface mounted, which makes it preferable when it comes to soundproofing. You will want to avoid using a can which will put a big hole in the ceiling (and soundproofing).