Well, I just have an eye for defects that I have a bad habit of assuming comes naturally to everyone. If your dad is familiar with cars, by all means take him along and get his advice. I wish I'd started listening to what my dad had to say quite a while back. Either way:
If you're serious about buying the car, go ahead and run a carfax on it. I've had crappy luck with carfax myself, but I have enough friends that swear by it to go ahead and recommend it.
Start with the outside. Look it over for any defects in the paint or dents. Twilight makes dents stand out, so looking at it in the evening is advisable. If at all possible, either get the car jacked up on jack stands, or on a lift. You want to get under it and look for anything out of the ordinary. Bent stuff and rust are key things here. Also take the time to check wear levels on the brake pads/rotors and tires. Check any of the rubber bushings to see if they're cracked and look like they need to be replaced. Look for any leaking fluids. The stuff will probably be dirty, but you should be able to tell if anything has been leaking. While it's off the ground, go ahead and spin the wheels to check if someone added a limited slip differential.
If it has rust, evaluate how bad it is. If there is some minor surface rust, it's not a huge deal, it's just something that will definitely need to be taken care of. Steer clear of frame rust. Look for any dents or damage to the frame rails or panels under the body. You can also check at this point to see if the drive shaft has been modified to a one piece unit (considered by most to be an improvement) or if there are any aftermarket suspension components.
Check the engine oil. Is it clean or black? Any weird gunk? Steer clear of weird gunk or coolant on the dipstick. The head gasket might be shot.
Make sure that the car is cold when you go to start it up. Check to see how it runs when it's cold. Ideally, it should idle fine and have no stumbling. Sniff the exhaust to see if it's running rich. If it is, the exhaust will smell like half burnt gas. If you don't want to sniff, then look at the tailpipe to check the color. Black and sooty is rich, a real light color usually means it's running lean, and a nice grey shade is what should be there. If it has the stock KA24DE, listen to it run. If it sounds like it you're rolling some marbles around in a tin can, then the upper timing chain guide is still there. No huge deal, it can pretty easily be removed. If you hear a knocking, tapping, or other noise that sounds suspect, either investigate further, or avoid it.
Ask to see any receipts for regular maintenance, including oil and coolant changes and any major maintenance including timing chain replacement and clutch replacement. I'm not sure off hand what the recommended interval for the chain replacement is, but I want to say it's around 100,000 miles. I may be incorrect, but if it has been changed, it's good to have a receipt for it.
See if there is any smoke from the exhaust, and if so, what color. Black indicates it's running rich, white is from coolant burning, and blueish/grey is usually from burning oil. The scent test for the trained nose can help in this situation, however the scents are nearly impossible to convey in words. Regardless, any smoke means that something has to be repaired.
Once the engine has warmed up, you'll want to perform a compression test on it, at the very least. A leakdown test is better. If you don't have a tester, then rent or buy one (or build one. I'm in the process right now of building a leakdown tester
http://www.xs11.com/tips/misc/misc3.shtml). The compression numbers should be uniform across all cylinders. A leakdown test will let you know where any leaks in the compression chamber are. If you do a little searching, there is plenty of information on the process to perform these tests, and they can provide you with a large amount of information about the internal health of the engine.
Check around under the hood to see if there are any obvious modifications or loose wiring. Check for any missing emissions equipment. If it's gone, it can cause the car to run rich. Check to see if the air filter is clean and other fluid levels. Check for any rust under the hood. Pay attention to the strut towers and battery tray, as well as the frame rail area. Look to see if there has been anything that looks like a recent change that might be there to cover up a problem. For example, a given area might have been cleaned up more than another to avoid detection of a slow leak in a component.
Go ahead and check the inside of the car. I'd suggest starting at the back and working your way forward. On 240SX fastbacks, the trunk likes to leak from bad seals around the taillights. Check the spare tire well for water. I'm not sure if this is a problem on the coupes or not, but either way, it can be resolved with a $5 roll of weather stripping from Home Depot (Believe it or not, that's what I was told to do by the parts manager at my local Nissan dealer. It worked.). Check for any modifications, including aftermarket stereo wiring and strut bars.
Check the upholstery for stains, burns, rips, and tears. Any funky smells? Any dead animals under the seat (It might seem stupid, but I found a dead rat in a Pignose Fastback I looked at buying.)? Is the dash cracked? Most of the S13's have a cracked dash. They've started making these coverlay things for them, but many folks just live with it. Ask if there are any aftermarket alarms added. Look under the dash to see if there are any obvious wiring modifications. Alarms can be OK, but I have yet to have owned a car with one that worked right.
Check to see if the idiot lights on the dash work or not. Also, check to see if the backlights come on when you turn the headlights on. The cluster should light up, the HVAC control unit should light up, and the push button switches should light up. If they're burned out, it's not biggie. I'm in the process of making a write-up for bulb replacement.
If the idiot lights aren't coming on, figure out which ones aren't working. If it's the CEL, I'd suggest you check the codes on the ECU to verify that someone didn't pull the bulb to hide something. If the CEL is on, check the codes. Evaluate accordingly. If any of the idiot lights either don't come or stay on, check the corresponding system to see if it's functioning properly. It could be a burned out bulb, or something worse.
See if the HVAC works. Run through all the switches and functions as well as heat and A/C. If at all possible, check to see if the rear defroster works, if equipped. Ditto for rear and front wipers, if equipped. Check to see if the pop-up headlights work. Bright lights are different on a Nissan than a lot of other cars. You have to push the switch away for them to stay on (something it took me a while to figure out). Have someone check all the lights on the car for you. If it doesn't work, check to see if it's just the bulb, or if it's wiring related. If so equipped, check to see if the HUD, power windows, and power mirrors are functional.
Take your test drive and listen for any weird noises. Does it bounce around when you hit a bump? These cars love to have rattles and whatnot from the body. If it sounds out of the ordinary, then check it out further. If it's a manual, rev it up a bit during shifting to check to see if the clutch slips. If it's an auto, see how well the transmission shifts (also check the fluid for scent and color). See if the cruise control works, if so equipped. Drive in a variety of areas, I'd suggest your test drive take you on the highway (55 mph at least), around town (35 mph or so) and stop and go. See how the car acts in each circumstance. Make sure the car doesn't start to get too hot. You've driven before... if it would seem out of the ordinary for your vehicle, watch out for it on the one you're considering.
If there's anything else to look for that I have missed, then by all means, someone add it.
If you do find some of the stuff wrong with it, don't stress too much. Smaller problems just come with the car. Some are easy to fix or live with. If you check those things, though, they will give you a better chance of noticing something big.