If you fly in to Milwaukee and don't want to rent a car, you can take a bus to Green Bay. It takes 2,5h and about $25 one way. But please be aware, that it goes only once a day. I don't know the schedule Milwaukee-Green Bay, but Green Bay-Milwaukee is at 6.15 am every day. If you decide to Fly in to Chicago, it takes you additionally 1,5h and $20 one way by train. Just visit
www.amtrak.com for further information on the schedule.
In Green Bay you have to pay gameday price for cabs on gameday and the night before. That means you pay $25 one way, doesn't matter if you have to go 1 mile or 5. Of course you have to do the Stadium tour and the Hall of Fame tour at Lambeau Field. Combination of both is $25. From bars perspective, I think Stadium View and Curly's Pub is a must see, but there are several other nice bars to stay around the Stadium (Anduzzi's, The Bar .....).
I heard there's a bus from Appelton to Green Bay at gamedays, but I'm not sure about the price and schedule. I only heard it leave right after the game which will cost you the option of attending after game parties.
Enjoy your stay in Titletown, you'll love it.