16" wheels for E30

For an E30 you want a 4x100 lug spacing, 57.1mm centerbore, and offset around 27mm, depending on wheel width. 

There are plenty of 4x100 wheels around for FWD cars, but they do not fit on E30's without spacers. 

Lots of E30's run Rota wheels, and there are usually deals out there on Slipstreams or RBs that are made to fit directly on the E30. 

Having had one for 7+ years, I would suggest sticking with the 15" wheels, as 16" tires are hard to find and 17's are starting to get big for the E30.  A 15"x7" or 15x8 will let you fit plenty of widely available, fairly inexpensive tires and give you a performance bump, but be a bit more forgiving.

If you don't pay attention to your sidewall height, going to bigger wheels can mean that you are going to a larger diameter tire. The practical effects of this are (1) your speedometer and odometer aren't accurate anymore unless you reprogram or swap them (no biggie for Lemons) and (2) you are effectively gearing down your car, which means that you'll get more distance per revolution, but it could hurt your acceleration too. Since the strong suit of the e30 isn't monster horsepower, you might want to consider if you want to hurt your acceleration potential. Or make sure to get a very low profile tire such that your overall diameter of wheel + tire is about the same as it was on the 14" tire/wheel combo. But those aren't going to be cheap, typically.

OTOH, it's not very difficult to find 14" Azenis that will fit your existing bottlecap wheels. The new K compound Azenis is getting good reviews. Ultimately, it is very unlikely that it is your wheel/tire combo that will have a dramatic effect on your result in a Lemons race. Sure, if your drivers are all very good and can stay out of black flag situations, and your pit stop procedure is down cold, then it's something to consider. But if you're a typical Lemons team, you'd be much better off spending the coin that you'll plunk down on new wheels & expensive larger tires on things that will make a real difference. Like driver training/practice days at the track. YMMV. Good luck.

Ah, typical street car mentality. Big is cool, big is better, big is fast. Nope not always true. Now they do look cool, but it won't necessarily make your car faster.

The problem with wheels and tires is they are heavy. And bigger tires and wheels are heavier. But you get more grip, right? Dilemma. You will get more grip with a wider bigger tire, but only up to a point. Its one of those diminishing return thingies. Yes a 205/50/15 is better than a 165/70/14, but there are other things to consider. A rule of thumb is that every 1 lbs of wheel/tire weight is = to 3-4 lbs of car body weight. Did you spend a whole bunch of time stripping out the interior to make your car lighter and faster??? So an extra 3 lbs per wheel = 36-48 lbs of car weight.

More on being heavy: Inertia. This is the energy in the rotating mass (weight) of the wheel plus tire. Did you swap out that heavy flywheel for a lighter one to get better acceleration (or at least you were thinking about it??)? By putting on heavier wheels its like putting on a heavier flywheel, exactly the wrong direction for acceleration.

If you know how to calculate inertia, you can make a rough model of a wheel (a disk, and a ring), and a tire (two side disks and a ring). then you can look at the rotational energy require to spin a 14", 15" 17", and do a 22 or 24" while your working the spreadsheet. Going up two or three sizes can really take a lot more energy!!!.

So more tread = good for traction, but a 350/45/18 on a BMW with 185 Hp is probably a waste of tire.
Bigger tire means more tread, good.
Bigger outer diameter = higher gearing, more top speed (up to the limits of the engine Hp), but SLOWER acceleration.
Smaller outer diameter = faster acceleration, less top speed (did you calculate your top speed for the straight aways?? you'll probably never be able to hit max speed on any Lemons track so you don't need top speed). the shorter the track and the more turns, the more acceleration you want.
Heavier tire/wheel combination = SLOWER acceleration.

So if you want to move away from the 14", go to a 15" and look for wide rims that fit under your car. Look at the outer diameter of the tires (its listed in the specs page on most tire sites) and find the smaller diameter. maybe a 16".

I understand the concerns about changing the gearing of the car and adding rotational mass, but we're not dealing with the stocker M20B25 in our car. We've got a Ford 302 swapped into it. Getting the tires rotating isn't our chief concern here. Plus, a few of our team members were hitting the shift light at the end of the straight at Thunderhill in 3rd gear (we're running a C4). We're not exactly geared for speed. That being said, we're not trying to make our gearing any taller. A 205/4016 actually shrinks our OD down 7/10", while a 215/45/16 takes us up 4/10". I'm not sure how much of a difference 4/10" of an inch will make, but I wouldn't assume it would add even 10mph to our top end. But I'm no expert by any means, so I may be completely off-base here.

What is our concern is the fact that Falken RT615k tires for a 14" rim have become difficult for us to get ahold of reliably. We've been able to get them before, but not other times. I know we don't want to add weight to the wheels adding unsprung weight and additional rotational force that is gonna work our brakes harder, but going with light rims might not actually make our wheels any heavier. Plus, the 205/40/16 Falken tire is actually lighter than the 195/60/14. And if we're gonna pay to replace the 14" wheels with light 15s, I figured that it would make as much sense to get some light 16s if we're already spending the money. Its gonna be a stiffer sidewall and a wider tire, both positives as far as I know.

The Rota Slipstreams look like they would work, and are pretty light at (allegedly 13.5lbs a wheel). Any other rims you guys have had success fitting to E30s.

15 X 7s are the way to go, cheapest and fastest, anything else is just window dressing.

Window dressing? Really? Don't you guys run 17's on the V8olvo? That's just for show....?

Not my idea,  it was done for gearing and traction and the 17s probably helped blow up the diff.

The Mishat car runs 15 X 7s

Possibly. We did literally just buy some 15" rims for our car yesterday, but if the price is right, I might snatch them up. Do you have pictures? And what is the weight per wheel? Our 15s we ordered are pretty light. So, I guess if they were cheap and light, I might pick them up. Let me know.

Surprised nobody has mentioned TRM wheels in this thread.  Specific E30 fitments, 15x7, 7.5 and 8, light, and dirt cheap straight from TR.

Designed for Spec Miata and Spec E30... I imagine pretty tough

$200 for one set, with tires that have been raced before but have some tread left. Plus shipping.