Yeah Raji, as wpr said, hotels usually want you to book at least 2 nights in GB. I don't know of any that do one night stays, which drives me nuts. However, if you stay 2 nights in GB, you are going to be able to experience the whole deal. No doubt. If you pop for two nights in GB, make a reservation now or as early as possible. If you do stay in GB, go to Kroll's East. It is way better, and the original. Do not miss the Packer HOF. It is too good to pass up.
A great way to go may be flying into Milwaukee, then taking the Saz's bus up on game day. You would have enough time to cruise through the Packers HOF, but your time will be a little tight. The best part is you don't have to drive. Drinks on the way up and on the way back, plus a meal at their tailgate. Worth every penny, if you just want to shoot in for the game then bail out. The drive back to MKE at night after a game can be long, and it is nice to not have to worry about it. Saz's requires reservations, so call ahead once you get your tickets to secure the ride up.
You could also fly into MKE and rent a car, buy a grill, or hit me up and I'll let you use one of mine, make your own tailgate, and really take it all in. Drive up at your own leisure, and spend all the time you want cruising at will through GB. Tailgating there is also something you will not want to miss. Great to be a part of that experience. Do you have tickets? Let me know what game you might be planning on and I'll see what I can do if you wish.
I've never flown into GB, myself. Either way you'll be stopping in Milwaukee. I love this city, and it is a fun place to stay as well. Can't go wrong either way.