Besides after a workout and before bed, what are the best times to take a protein shake?

As for post-workout, this is not entirely true. There is no sudden burst of muscle-making after a workout. Building muscle tissue is a 24-hour process, so getting adequate protein throughout the day is far more critical than the window after a workout. You simply need a few grams of protein to replace what was burned as energy and you're good to go. The most important nutrient after a workout is carbohydrate. While muscle rebuilding takes place over 24 - 72 hours following a workout, there is a window of a few hours where your muscles are "primed" to take in carbohydrates that were depleted during training. For this reason, you'll find the more superior-formulated post-workout shakes (i.e. Mass Maker from Beverly International or Surge! from BioTest) contain about a 2:1 carb-protein ratio to supply just enough protein but plenty of carbohydrate to refuel your muscles.

Aside from perhaps extra protein (and again, getting it from whole food sources is superior, but if you are having trouble consuming adequate protein from whole foods, then supplementing is certainly fine) a quality multi is beneficial, not a topic for this thread, if you search, you'll see tons of conversations about this.

For your protein before bed, I do not recommend whey, unless combined with some sort of fiber or high quality fat. Whey is a fast-absorbing protein that can rapidly be converted to energy rather than used to build tissue, etc. You want something slower-relasing, like a whole food protein or if you get a shake, a blend that contains some casein, perhaps hydrolyzed beef plasma, etc. I use a brand from the company I represent that is simply a soy protein powder. Another great source would be Muscle Provider from Beverly International - a top quality blend that tastes incredible.