I wrote this on the other play date posting, but I saw your post and figured I would post it here as well. I hope it helps.
I know that I am always busy and have a hard time getting to set up play dates as well. But I did find a place for mom's that may not be able to keep a scheduled play date with others, but still have their kids interact with other kids. It's an indoor playground for children under 5 years old off of Tudor. It's called Park & Play. It's on the east side of town. Here is the website if you want to check it out: