Placing my car in neutral without keys

Look for a shifter release near the shifter.

As long as you understand the inherent danger of doing that, there is usually (on most vehicles) a way to bypass the shifter interlock, sometimes by pushing a pin or slender rod in a small recess on your shifter console, just google your make/model vehicle and "shift lock release" or "bypass shifter interlock". You should know that if the vehicle is on any kind of incline, even a very slight one, it can start rolling and you will NOT have the benefit of power brakes to stop it. So again, it can be dangerous to force a vehicle out of park without the key. They also make wheel dollies for sliding a car around, Harbor Freight has them cheap and they go on sale often.

Set the emergency brake and chock the wheels.