Someone in this thread mentioned spacing rooms to save money on elevators. That's good but I have since realized it has a much greater benefit: preventing fires / roaches / moles from spreading. If a room borders nothing but an elevator, disasters don't spread!! Which means you can rush endlessly and simply evacuate a room and wait for the problem to go away, instead of wasting dweller health dealing with the disaster. The exception is that training rooms that border each other aren't as risky because you can't rush a training room, so they have disasters far less often. So if you're going to stack rooms, stack training rooms and space utilities.
High Health Rooms First
At some point in the game Deathclaws will start to attack regularly. They kill low level (level, not SPECIAL) dwellers quickly because low level = low health. So think about which rooms you have that often have the highest level dwellers in them. Maybe the utility rooms? For me, it's utilities and also the luck room (lounge) because I like to make sure my highest level explorers have maximum luck. Whatever rooms are usually full of high level players, put them near the vault near. You usually train new dwellers in strength, agility, and perception right? So the gym, agility room, and weapons room are usually full of low level dwellers. Think about that when laying things out.
First Room After Vault Door Should be Water Plant
I think this makes sense because higher perception increases aim accuracy. So if you have a 3-wide water plant with six people, and they all have great guns and good aim, that's a great way to greet raiders.
Put a Big Room Near the Vault Door
Doing this allows the first room raiders enter to have six people. I arm these six people to the teeth and it's worked out well so far. The opposite would be to have the first room be a small room with two people, in which case you'll be outnumbered and will take more damage than necessary.
Food/Water Next to Power Plants
Rooms like living quarters, med bays, and training facilities should never touch a power plant. Such rooms do not belong next to, underneath, or on top of a power room. Try to have the closest rooms be food production and water production rooms. If the power goes out, the closest rooms (production rooms) stay lit and the non-essentials go dark.
Big Rooms Are Risky
You can combine three smaller rooms of the same type, to make one big room. The incentive is to save caps, because upgrades are cheaper this way.
The problem is, if you have only 2-3 people in a 6 person room, you hit "rush", and it fails... you may be in trouble. The failure accident will be proportional to the room size and your room is far from fully staffed. A handful of rad roaches or mole things can kill an understaffed room pretty quick if you don't get them help.
Plan for the Worst
When you fall behind in power the rooms further from the power plants loose power first. When the furthest rooms are water and food rooms and they go dark, things get ugly quick. Avoid it.
When you use smaller power plants, you have better damage control because you can rush the rooms closest to essential utilities.
Also, early in the game having only one big food/power/water room is risky because that's only one or two chances to rush. If you have 3-6 small rooms, you can fail a couple times and still keep trying.