apartment therapy changing the world, one room at a time

I would use two wood triangles large enough to go from edge to edge cut to the angle that you want the mirror to hang, mount them to the back of the mirrors. The triangles would then become the mounting surface to the wall and create the space to hide the lights and the wires. Glue and screw for best results.

Easy: 2 heavy duty o screws placed 1/4 to 1/3 down each side of the mirror, depending on how much tilt you want. Then string slack wire between them and hang. Depending on the weight of the mirror, you should use heavy duty hanging hardware and try to drill into a wall stud. Alternately, just buy a lighter weight mirror - the ones at Ikea are fairly light.

You could create a hidden "ledge" by putting two picture hangers (like these) on the bottom edge of the mirror. Next, rest the mirror on two (large) screws in the wall. To create the tilt, screw some eye hooks (like these) into the wall, then run picture wire through the hooks and the hanging hardware at the top of the mirror so the mirror hangs at an angle. In order for the eye hooks to be hidden, you may have to move the hanging hardware on the mirror further down towards the middle. It would end up looking something like this.

I like streepyj's suggestion for how to hang at a tilt, so I'll just address how to possibly do the lighting portion.

I would suggest looking into some battery operated rope lights or christmas lights that could be affixed to the mirror backing, and turned on or off by a switch or battery removal. That would prevent needing to run any wires down the wall, and the pocket created by the angling triangles would leave space for the lights to be placed behind the mirror.

You could also create a ledge with a book shelf. Just a thought.

I did something similar by attaching "piano hinges" along the bottom inside (you can get them at the hardware store in varying lengths), and then used a window casement stay to control the pitch of the mirror on one side...looks *REALLY* slick!

I recognize this place as Union Restaurant on Washington St.
I have been there many times and enjoyed the food.
You could rest it upon wood trim and put the wires in the back.