A super quick baby blanket, one that can be used in a variety of ways is the self-binding baby blanket.
https://www.youtube.com/watch?v=ZFnXashT_rs
This video is a quick tutorial or you can search YouTube for others. I like to add a small square in the center when I'm top stitching to help keep the two layers from slipping.
It's so quick and easy you can make a few. Adjust the sizes so the new mom can use them for swaddling or putting on the floor for tummy time. Of course, if you're looking to make a keepsake quilt, these won't do.