parking lot before the game, just look for the crowd on the Eastern side of the stadium (if the players are still are parking above ground)
You can see them drive in and enter players only lot..Might get lucky to get an auto as they are pulling in.
The tailgate is personal preference. Big ones are okay, food and drink but lot of people and need to walk back to stadium.
If your out going you can prob go up to a group and explain your situation and bring a 6 pack.
This might be better since it is your 1st time there..Get the feel of TRUE tailgating..Walking around and going to the different tents they have set up on the EASTERN side. Sometimes this area has retired players-
Stadium tour
http://www.packers.com/lambeau-field/stadium-tours.html
I do not know of any cheese tours, but I am sure someone here does