For different circumstances you would use different forms. Here are some instances.
• “Come to my room”: While away from your room, you tell a person to come with you to your room; or via telephone, tell someone to come to your room.
• “Come in my room”: Standing outside the door of your room talking with someone, you ask them to come in to continue a discussion. But typically it would be stated more briefly or at least differently: “Come in”, “Come on in, let's sit down”, etc without mentioning the room, since it is right there anyway. Note, into is a likely prospect when the room is mentioned.
• “When I came in the lobby in the evening, there were tons of people gathered around...”: This form is inappropriate; use into instead. I'd use into for going into a lobby from inside a hotel.
• “When I came to the lobby in the evening, there were tons of people gathered around...”: I'd use to for going to a lobby in a hotel, from elsewhere, but typically no real distinction will be made between use of to and into in this context.
• “When I came to in the lobby in the evening, there were tons of people gathered around...”: This form is appropriate if you passed out and are regaining consciousness.