They wonít necessarily have spaces to book but The Raeburn has so many no shows that youíd probably get in. I got in twice on Saturday without a booking.
The Antiquary along Stockbridge also has outdoor seating which you canít book. Saturday afternoon it was dead so it would maybe be worth trying there.
Neither of them youíll be able to get a booking though so not something you could guarantee!
Also heard that The Beehive and Last Drop on the Grassmarket have regularly had loads of tables free if you walk up although havenít seen that myself.