Do you remember that song by Lynyrd Skynyrd? 'Gimme three steps, gimme three steps mister, gimme three steps towards the door.' I try to remember that song when I am moving on stage during a public speaking engagement.
When you are moving on the stage, make sure that your movement has a purpose. If you take a step, go at least three steps in that direction to cue the audience that you are moving for a reason. One of the biggest problems I see, even when coaching top speakers, is that many of them wander around or take a step here and a step there. This is extremely distracting to the audience.
When making an important point during a speaking engagement, move toward the audience. Three steps forward from center stage would be a very powerful position that would command attention (especially if you walked right off the stage and fell on your face -- hahaha).
Upstage (away from the audience) left and right are weak positions. They can be used when you feel you are overpowering the audience or when you want to remove attention from yourself. I use these speaking positions when I direct the audience to do some task, such as talk among themselves.
Upstage center is a strong position, but one that makes you appear disconnected from the audience. I usually avoid this position.
When I want to be playful and/or really get the audience involved, I'll go right into the crowd. I might have to come down off the stage, but to me it is worth it. Good public speakers get really connected and I feel like one of them when I am out there. I am also sending a message that I really know what I am doing. I don't need any notes. I don't need any visuals. I don't need anything but interaction with them. They love it!
The main thing you have to watch out for when you are out in the audience is that in large rooms with lots of attendees many people can't see you, so they start to lose interest if you stay out there too long. This is counteracted if you are being projected on a large screen and you have an on-the-ball and well-rehearsed video crew. (If you don't alert the video crew ahead of time of your intentions, they will be scrambling to follow you and it won't look good on the screen.) You will probably be lit poorly too. When you are being projected, think about toning down your overall movement because it's not easy to follow you wildly around the stage with a video camera.