We've all put on a movie with no intention of actually paying attention to it. At least this time you can be real upfront about what's going to happen.
The movie is just background noise and a small distraction while you and your date get snuggled up and comfy. So grab some blankets and extra pillows, select a random movie (tip: try not to choose something with a bunch of crazy shootouts or action scenes) and start sawing logs.

I'd like to say that anytime is fine for a nap, but there probably are some times when you should be alert and wakeful. However, once you've narrowed down when you can schedule to be lazy, you should jump on that opportunity. And by jump, I mean fall asleep.

Unless you're a horse or a person with the unique ability to sleep in an upright, standing position... then pretty much any relatively flat, moderately comfortable area that's large enough for 2 will do. Personally, my preference would be to make a "super bed" which is basically just a spot on the floor that you've comfyfied with pillows, blankets, sleeping bags, etc. Granted, the bed or the couch are obviously suitable options as well that require less upfront work.