The doctor asks if Marcus could stay with them and Will jokingly asks Suzie "my place or yours?". Now that's a line you'd rather ask a date you're going to hook up with and Will says that exactly as a joke to Suzie, playing with that meaning, who afterall was his date before the tragic events unfolded. But soon enough, and with the help of Suzie's confused or even disapproving look, he realizes that this was quite an inappropriate situation for such a joke, so he apologizes immediately afterwards. It's just supposed to be an awkward situation where Will makes an insensitive fool of himself.
And after that, he drops Suzie, her daughter and Marcus off his car and leaves them, so it's pretty likely that Marcus stayed at Suzie's that night. It's unlikely for Suzie to leave him alone at his own place after such an event, especially since the doctor asked if he could stay with them.