Thanks AS and Tallula, would it be okay to ask her out to a friendly dinner? Certainly not a date, but I would make it clear it would be just to make our last week together a friendly one.
I don't see the harm, but just remember not to have any expectations. If she says "no" then don't act disappointed. I ask my W to lunch on the weekends all the time, I just tell her I'm taking the kids out and ask her if she wants to join us. She does about half the time, but when she doesn't I just say "no problem!" and continue the convo like it's no big deal (which it isn't). That's the place where those kind of invites need to come from, it's like your asking a friend to join you. If they can then cool, but if they can't it doesn't make you mope around, because you know there will be more opportunities in the future.
