SRT-4 rims are only 6" wide, just like stock Neon rims. Like others have said, its the combination of tire height versus perch height on stock Neon suspension that make them not "fit"...

 

What that makes no sense to me, the 18's on the car right now are 18x7.5 with 215/35/18 tires and my srt rims are only 6 in wide, so how could a 6in wide rim have the sam width as the tire on my 7.5in rim????

 

Tires are reasonably flexible in terms of what width of rim they will fit on. Typically any given tire will fit any width rim to about +/- 1" of it's designed ideal width. So they'll fit a range of wheel widths about 2" across (this varies a bit depending on specific tires). Also the taller the profile (height) of the tire, the more flexible it is in what size wheels it'll fit on. 215/40/R17 would be really stretching to fit into a 6" wheel, I'd venture to say that some models of tire in that size wouldn't fit. Meanwhile they'd fit up to an 8" wheel at the wide end. Most tires in that size are 'rated' to fit a 6.5" to 8" wheel width. I'm sure they can be mounted on 6" wide rims, and there's more traction with that wider width tire on there, but there's also more risk of popping a tire off the wheel in panic turn, and more edge wear on the tires, because there's not a lot of shoulder support for the tire. On the other hand, if you catch a curb, there should be enough tire hangover to keep you from scratching the rims up.

Tires which are wider than the rim have a slightly 'cushier' feel to them, while tires which are narrower than the rim have a firmer ride and can withstand more lateral G-force in extreme handling. Of course different models of tire are themselves designed to be more or less plush or firm handling too. These factors sort of add up, with your suspension system, to give the end result.

The limitation of tire/wheel size on NON-SRT neons is a sort of diagonal restriction. It's not really a wheel width limitation as 7.5" wheels fit just fine (note that both regular and srt models come with 6" width wheels though). But the tires cannot stick out more than a certain amount inward & upward into the wheel well at a diagonal angle (mostly upward). note that 205/45 R17's and 215/40 R17's should both clear the limitation, and are both very close to stock diameters (185/70R14 or 185/60R15*SXT* or 195/50R16*RT*). On 6" wide rims, 205/45's would offer a slightly firmer shoulder support for the tire, and the 215/40's offer a bit wider traction area on the ground. For firmer handling 215 width tires, getting 17" by 7"or7.5" wide wheels would give a lot more shoulder support to the tire. But you'd be putting pretty much the same size tires on em as you would on the 17"x6" (else you'll rub). The SRT-4 comes stock with 205/50 R17 tires, which are a tad taller than the 205/45's or 215/40's. Stock SRT tires will rub, but there's nothing wrong with running 17" wheels, just gotta narrow the tire profile a smidge.

The best of both worlds might be 215/40 R17's which are Z-rated to maintain firm handling. But Z rated tires have less sidewall flex, that size might not squeeze down very well into a 6" rim with those stiff sidewalls. hard to say for sure without trying on a brand by brand basis. Personally I'd run 205/45's myself, I mean if i had a set of 17" SRT wheels. If I had 6.5" wide (or wider) wheels i'd go to the 215/40R17's though.

I had an 04 RT, came with 16"x6" wheels stock, and 195/50 R16's. I ran it with 205/50R16's and 205/55R16's just fine, and I know of people putting 215/50 on the 16" rims. The RT is geared a little TOO low, especially in 5th, so people tend to upsize the diameter when getting non-stock tire sizes (tire diameter affects final output gear ratio). But 215/55R16 is just too big on the RT, i know first hand that that size rubs. Which means 215/45R17 would also probably rub as they're very similar size in terms of exterior dimensions.

generally 1" of wheel diameter is equal to roughly '10' in the second tire size number, so 205/55/16 is very nearly the same height & width as 205/45/17. The first tire size number is the width, but oddly it also affects the final diameter of the tire, such that 10 in the first number is equal to about 5 in the second. so 215/40/17 and 205/45/17 are different widths, but very nearly the same height.

Also... aftermarket wheels can have a different offset than stock wheels do. This *could* put the wheels slightly further out away from the wheel wells. That could impact what size tires may fit the car.

If money is no object, get lightweight aftermarket 17"x 7/7.5" wheels in your favorite style, with 215/40 tires (or as srtgtr34 noted, 18"x7.5" wheels with 215/30 tires).
If money is somewhat important, buy some 'hand-me-down' SRT 17x6" wheels from someone who's pimping out their SRT with new wheels, and put 205/45 tires on them.
And last but not least, stock SXT 15"x6" aluminum wheels aren't 'bad' exactly. They're very lightweight, and you can fit V or Z-rated 205/55R15's on them. 205 width is a LOT more traction than 185. And Z rated tires would give you firmer handling. They won't look as cool, but road itself won't be able to tell a huge difference.
edit: i just checked tirerack.com, didn't see any Z-rated 4 season tires in that size, but plenty of V rated ones (V is the next best thing). They had V rated Michelin Pilot Exalto's & BF Goodrich Traction T/A's in that size, both of those are really nice all weather performance tires.

oh, another thought... if you get new wheels you can put 'summer' performance tires on them. "Summer", non-'all weather' tires have noticeably more traction on dry pavement, average traction on wet pavement, and 'zero' traction on ice/snow. Then put all season tires on your old wheels. Then each fall before bad weather hits, swap your old wheels back on, then back to your custom set with summer tires in the spring. Its a bit of work, but summer tires do ride/handle/grip really nice when in their element.

so yeah, that's the exhaustive answer

 

WOW, lol. thanks for clearing that up, it has always intrigued me. I did end up getting 205/45/17 for the srt wheels, they do fit nicely but they do hit when I turn the wheel all the way.

 

do they rub at full turn? that must be just teasing the edge of what fits then, my RT with 205/55R16's didn't rub and that's 'nearly' identical exterior tire dimensions.

Really, that's kinda big diameter for a base or sxt neon, like an inch taller than stock. The RT & SRT both have their own torquey gearing so took a bit larger tires. I'm guessing you added some oomf under the hood to balance everything out? That size must be great gas mileage with the base model transmission.

 

Its a little worse than a tease, but I rarely have to trun the wheel all the way so I don't worry about it

 

I know this topic is old, but I've got a new neon and its become relevant my R/T had pretty nice 16" wheels so i left well enough alone, but it's successor, my new sxt, has 15's and they look kinda small. i'm going to get it some 17" wheels.

You say 17" 215's fit if they're /40?
do they rub at any?
also what is the offset?

I'd love to go with 215's if they'll fit. otherwise 205/45R17's like srtgtr34 has.

 

When I took the srt wheels off and put the snow tire on I saw where the tires hit. The left tire was rubbing the inner plastic fender well only when turned to the right, wasn't bad. The right tire was rubbing the metal inner fender well where two peices of metal joined only when I turned to the left, which doesn't look to be in a good area for the tire to rub, I would say it was moderate. I think this is due to the design of the tire and not with the actual tire dimension. Both rub area's where about 1 sq. in big which really isn't to bad. Now that I think of it, it has to be the tire design because my old 215/35/18 had no problem fitting and didn't rub at and they had a wider sidewall.

 

for 17's on a stock setup you want to go with 205/40/17