Go where you usually eat!
Just go into your local boite and talk nicely and see if they'll let you hold a small wedding between service (before lunch, before early dinner). We suggest you don't start out by saying "wedding", but ask if they have a quieter table for a small 'presentation' or 'celebration', then you can let them know it's actually a little private wedding ceremony, no confetti, no fuss or muss, just standing in the corner for 15 minutes, and then champagne and signing things...
We've used Le Select's back terrace as well - reasonable with a prix fixe menu - a delightful wedding. And the Bistro at the AGO let us have a small elopement (6 people) at 4, just in the back when they weren't busy. We had a fun wedding in the basement of Rodney's Oyster House (just 20 people). Here are some other ideas
Sometimes you have to use your imagination - a snug at your local pub, the window area of a cafe, the upper room at a bistro, the back patio or garden of your favourite brunch place. Just chat with the staff. If you have more than 6 people in a smaller place that does not have separate "event" staff, they will probably need to assign a staff member as your waiter/server, and they may need to re-arrange tables before and after, but as long as you indicate that you're willing to order drinks and not put too many extra demands on their staff, they'll be willing to consider your event. You might start a trend!