I agree that 18 months is a hard age. I understand why you want a drop-off program and why it'd be good for you and your kid (we wanted this, too, at that age), but I don't think there are many programs like you're seeking for this age.
At age 2, you can start a preschool a couple of days a week, but 18 months is trickier. (And most preschools operate on a school-year basis, so you start in September, and the kid usually has to be 2 by Sept 1 or Oct 1.)
One option might be to start your own playgroup with other parents -- or a sort-of babysitting exchange with others in your area. I almost joined one and thought it was a great idea, but my kid ended up being way younger than the other kids at the time, and I wasn't quite ready for it yet. I think he was only about 8 months at the time, and I was hoping to find something for when he was 12 or 15 months. You could easily arrange this even with one other mom -- where you agree to drop off your kid at her place on Tuesday mornings and vice versa on Thursday mornings, or whatever.