My hospital was the same way. One room for labor/delivery and one room for recovery. Here is an idea of what I took.
Labor/delivery: Snacks for DH, therma-care back wrap (I used for shoulder pain because I had contractions through my shoulder after I hap my epi), phone chargers, our tablet/computer & charger, camera, headband, and pillow for both me and DH (we are germ freaks so we had our own pillows)
Recovery/pp room: I sent DH to the car once we were moved and he got our bag that had clothes, tooth brush, shampoo/conditioner, body wash, snacks, water jug, hair brush, nursing bra and boppy.
Then once we found out we were being discharged he went down and got our baby bag and carseat.
Also, keep in mind that you may be there for more than just the 24 hrs. We had an emergency induction on Thursday and we were able to leave until Sunday evening due to LO having jaundice and I was GBS positive. So, make sure you have extra clothes just in case.
Hope that helps =)