While I've never eaten alone at Palo, I have done so at many restaurants when travelling for business. I like to save the bulk of my per diem to eat at a nice restaurant. I actually kind of enjoy it. Bring a book, check out the view, strike up a conversation with the wait staff (who, at Palo, are really nice and eager to talk to you). I would definitely encourage you to go by yourself, even to do both brunch and dinner.
I do think you'll be made to feel uncomfortable at all, only as much as you allow yourself to be. People will not be pointing at you and saying, "look at that person eating alone!"