Yes, you may surface mount a box. The hardest part will be drilling the hole in your masonry to run the wiring. I would be inclined to use a short piece of conduit to protect the wiring and make it easier to seal up around the wall penetration to avoid water and critters getting in.

Some things to know:

1. Outside receptacles must be protected by GFCI (either being GFCI themselves or downstream of such a device).

2. The box needs to be rated for wet locations as does the cover for it. Modern code requires the cover to be an "in use" cover that allows for it to remain dry even when cords are plugged in.

3. You may tap into other circuits with certain exceptions. The receptacle circuits for kitchen area small appliances, bathrooms, and the laundry area can't be shared with these. Be sure it is a 15 or 20A circuit, and if it is a 20A circuit that you use 12g wire.

Modern code requires at least one outside receptacle in the front and one in the back of the house. If you're going to do this, you might as well do both.

Excellent! Thank you!