I have ironed in my rooms at Bally's and Paris, no problems. If you add water, make sure it is bottled and also let it steam on a towel first to make sure any debris doesn't ruin your shirts.
I've never had any trouble at the Golden Nugget, Wynncore and now Hard Rock. Those three-(3) properties pretty much cover my monthly stays back to 2003 or thereabouts. Since I have daily meetings while in town, I use the irons a lot... though I try to get away with just steaming the shirts in the bathroom, it doesn't always work.
I know I am not telling you anything new here suggesting a dry cleaner -- my husband always takes his casual Columbia shirts to the cleaners before we go and gets them dry cleaned and pressed. He hates to fool with ironing and they hold up very well for the trip--nice, crisp and wrinkle-free. If you only take a carry on and roll or fold your shirts -- that of course probably wouldn't work.
Downy makes a wrinkle release spray that works enough for us. I spritz the garment, hang it up in the bathroom while we shower with the fan off. Seems to do the trick.
I'd avoid using steam, and obviously check the bottom before you use it, but otherwise I've never run into a problem with in-room irons. I use the rollup method of packing, so my shirts usually arrive OK, but there's nights when I get back to the room and just throw a shirt on the bed instead of hanging it up, so you can get a couple of creases. I don't bother getting the ironing board out, just iron right on top of the bed, lol.
There are assorted tips online you can find on packing things so they don't wrinkle. Also with clothing less formal than dress shirts, you can often get a lot done just by running the shower on hot with the shirts hanging in the bathroom. Beyond that, usually I find the irons fine. the ironing boards though can be annoying, as they are often those half boards, and tabletop.
Two words: permanent press Or hang your shirt for the day on a hanger in the bathroom while you shower and let the steam do its thing.
The irons at GN are fine Breeze. You can get some distilled water for about a dollar down the street at Walgreens.
That's an excellent tip... I screwed-up a shirt once... the iron had been set on plastic or something and immediately stuck to my shirt.
I give all my shirts to the butler immediately upon arrival to have them all pressed. The steam shower also works great for removing wrinkles. Hang up your shirt / pant while the temp is warming up, wrinkles out in a few minutes time.
Growing up w/well water, my parents always used distilled water for ironing. So I do always use that or whatever bottled water we have in the room. Water w/impurities does some terrible things if you turn on the steam function.
I was going to suggest this as well. Also, hang them in the bathroom. The steam from the shower will help get any out as well.