An average of $22.50/mo for two adults in Minnesota (lots of winter layers).
I just looked at Mint to answer this question. I generally put about $50 on our laundry card when I fill it, and I filled it in March, May, August, October, and just a couple days ago. For the $205 total since the end March, I guess that's an average of about $22.75/mo. Our machines are $1.50 per wash and dry, and sometimes I wash two loads and dry them (or mostly dry them, which I call 'fluffing' them) on the same drying cycle (1 hour on the hottest temp is too long for most of our clothes, so I'll do 30 minutes for whites, and 30 for darks/knits, and hang things on hangers so they don't wrinkle, plus nothing gets crunchy this way).
DH and I both re-wear clothing when possible, and an apartment that including a washer/dryer would be significantly more in our area (like $200+ per month), plus farther away from where we need to be.