At that age I just sat with him and talked and sang and made faces at him. I'd also go for little walks with him in the sling because he likes to look around.
I just carry him around and talk to him about what I'm doing, what are plans are for later in the day, etc. I use his name a lot so he'll learn to recognize it. We make eye contact, have tummy time, and that's about it. Baby's First Year Week by Week says this is play time for a newborn.
I talk to him and kind of just narrate what we doing...like during a diaper change I kinda sing as goofy as it is "we're gunna put a clean diaper on your butt on your butt on your butt". I also have a toy with flashing lights and music that he likes to watch as I move it around in front of him and he loves to just lay on my bed with him and stare at my face as I make goofy faces at him or just smile and we do a lot of dancing to music (he LOVES The Hussle! Ha ha). It's fun to make the faces at them and see how they learn to mimic you :-) Just talk to them, play music and dance with them or go for a walk
Sing, talk, tummy time, making faces. I'm pulling out some of DD's old infant toys today for DD2 to look at (and as a way for DD1 to learn how to play gentle with her too).
Re: Newborn "play" time