I never had these when I gave birth (and let's not get started on the disposable, mesh hospital undies), but if I had, they would have been a game changer. The Nyssa brand features a pocket for an ice or heating pack, is super stretchable, and just looks really comfy.
Get it from Nyssa for $32.
I'm also a big fan of Llama Momma's "Mommy Bag" for moms, which includes a changing table and is just plain cute.
Get the large bag from Amazon for $129.99 and the clutch is $39.99.