This is something I've thought about a good bit. As have a lot of us I'm sure. We know of at least 2 I think AWD converted B13s, and at least 1 AWD B14. There is 1 known B13 RWD conversion but that is a much harder task. I'll get to that later.
Front Engine AWD - The easiest way to do this I believe is to get a narrow-block SR20, and an AWD transmission (with transfer case). The narrow block SR20 engines came in any SR20 car that had AWD as an option. This includes the BlueBird and GTi-R obviously, but maybe the Avenir and Primera too?
So once you have the engine and transmission, the driveshaft is your next thing to deal with. I believe a GTi-R driveshaft might work, but you might have to go custom. Then you have the fuel tank to deal with. Again the GTi-R tank might work, but I think most people go with a fuel cell.
You'll need to find a place to run the exhaust since the center tunnel will be filled with drive-shaft now.
At that point the rear suspension, rear diff, and halfshafts are your last concern. The GTi-R stuff basically bolts up I believe, so you're home free. It might take a little bit of fab work out back, but nothing too bad.
Forum member
@BusinessMan_24 did this with his B13 (NX2000). There is a thread around here on it.
As for RWD, things get a little more complicated.
Front-Engine RWD - You'll want a RWD SR20 setup, with a RWD SR20 transmission. You have to deal with the driveshaft issue, which probably means custom. Same issue with the fuel tank here as it will get in the way of the driveshaft, so go with the GTi-R fuel tank or a fuel cell. The rear suspension, diff, and halfshafts could be used again from the GTi-R but you might want to think about working in an S-chassis diff into the mix to handle the torque.
The firewall will need a good bit of work to make room for the RWD transmission placement. You will basically have to create a transmission tunnel from scratch. You're then going to likely have a hell of a time figuring out the steering rack. This is probably the biggest issue with the least research done. The RWD engine layout and transmission will need to use the space that your current steering rack occupies. The steering column may need extending or other work depending on where you decide to put the steering rack.
You'll need to find a place to run the exhaust since the center tunnel will be filled with drive-shaft now.
And then of course you'll have to create the engine and transmission mounts for the RWD setup, but that shouldn't be too hard.
Get ready for chassis flex up the wazoo.
Mid-Engine RWD - You could always attempt this style of conversion which will mean putting the FWD engine and transmission basically where the rear seats and fuel tank would be. You'll have to fabricate a support frame for the mounting and convert the suspension style to one that will accept the engine in this configuration including spindles/knuckles that accept halfshafts.
A fuel cell would likely go up front where the engine used to be, and you'll have to run some long radiator hoses, etc.
This style has actually been completed by one of our forum members
@OnTheChip but it was in an Integra, not a B13.