first...we establish some common nomenclature:
15" is simply the outside diameter of the wheel.....that is not a factor in whether or not it'll work on your JK. I went from factory 17" to 15" and have no problem.
The point people make when they say 15" steels wont fit is that SOMETIMES the Backspace isnt deep enough to clear the calipers.
Thats a new term....backspace. If you lay a wheel flat on its back on the ground, the "Backspace" is the distance from the surface of the ground to the back (bottom) of the mounting face of the wheel.
The smaller the backspace...the more shallow the clearance. I may be wrong but I think the magic number for clearing the calipers on the JK is 4.5" You want that or more. Less will rub.
So...wheels...15" diameter...no problem....4.5" or more back space...no problem....at least 8" wide....no problem.
Now wrap that sucker in some rubber. Here is where the options go wild.
Jk can mount 33" tall by 12.5" wide tires without lift. They look good and work great. I off-road ever day and never have a problem. But Im doing it for a living, and not for fun. Recreational wheelers look for tough spots where more clearance, lifts, bigger tires could be useful. I dont do; that so I cannot comment on it.
Again, I'm talking outside dimensions of the tire. You can have alost any sized wheel inside that tire. You said you like 15" (so do I) so I am gonna concentrate on that.
There are virtually endless options for tires. almost any of them are good. a few are great. and some are bad. most tire websites have consumer reviews. It can be fun...and monotonous research.
Just like shoes for your feet...get tires that fit your needs. If you are going to be on asphalt a majority of the time...you might wanna look at All Terrains as opposed to mudders. They are smoother and quieter and typically last longer. At the same time, mudders sure look nice on a jeep.
Personally, I run Falken Rocky Mountain (aka wilderness) all terrain 33x12.5 on 15" Chaos 5 from Discount Tire and couldnt be happier. I drive 160-200 miles a day. 80% Pristine toll road at 85mph. 10% gravel roads at 30mph. 10% rock trails cactus and mesquit at 1mph. Works like a champ.
Similarly....others swear by their brands. To each their own. No matter what you choose, I promise that they will not be the last tires you buy.
Learning what you like is MOST of the fun.
Happy trails, all.