How to install an outdoor outlet in new stucco (not retrofit) -- with details done right

There are “old work” boxes made of metal Grainger here is just 1 the home stores will have less expensive models that work fine. The type of electrical box outlet? This is where you want to spend a few dollars more and get a good one with a metal cover that allows the cord to come out the bottom with the cover closed. If you don’t like the foam a piece of rubber sheet can be cut to shape and put in place of the foam seal that will last for many years. Here is a while in use cover I use weather tight I just used this site because I found the items quickly they can be found much cheaper at other stores.

Just hear me out, you'll see. You'd still use an exterior grade plastic box & matching cover, because you can't get those in metal or any metal that you would want. The matching box & cover are crucial as you need the mounting holes to lie-up & sandwich the stucco on both sides.

Like the box pictured below, you'd screw through its side or back into a stud or blocking. Then, the cover assembly would be caulked or siliconed to the stucco prior to screwing, with Stainless Steel Screws, it to the box.

This, keeps the stucco as an impervious barrier to protect the in-wall box & allows for water to only flow around the separate cover assembly. In the future the cover assembly could be easily removed & re-caulked or siliconed, if needed. Also, bevel the bottom of the stucco opening outward like a windowsill to ensure water can't enter.

Now, the final trick is to cover all of the exposed plastic with a Stainless Steel Blank cover plate with Stainless Steel Screws, Bolts or Pop-Rivets attaching the cover plate to just the hinged door's face. You'll need a gap at the top for door operation & at the bottom for a finger pull. You may have to go to a 2-gang blank cover plate or sheet Stainless Steel to cut down & bend the edges in for a proper fit & clearances. But, all UV damage will be eliminated.

These boxes by Arlington Electric are wonderful for exterior stucco walls.

Arlington In-Box

Arlington In-Box

Quickflash part E-AIB is matching flashing product, for helping water behind the stucco pass the box without damage to the wood:

The main issue with stucco is that it's never waterproof: there will always be cracks, and always water dripping down the water resistant barrier behind the stucco.

If you want the in-wall look, consider a molded flashing product, to allow proper overlap of the building paper for drainage. Quickflash makes several, such as model E-SGB-C: