For hotels, you can stay in Appleton. It is a D III college town about 30 miles from Mecca with a 4 or 6 lane road connecting them. They have bars if you like that. A mall and lots of places to eat. They have a ton of inexpensive and moderately priced motels.
As was mentioned just a short trip down the highway is Oshkosh. It is about 50 miles away on the same road. Legal speed is often 65 mph so it doesn't take an hour unless there is an accident. I see them from time to time. Yesterday it was on the bridge heading from Oshkosh to GB so we were kind of stuck for about 25 min. Rooms are less expensive here. I stayed at a Super 8 with my son. Mainly because by the time I booked a room there really wasn't anything closer for less than $150.
As I said traffic is normally pretty good. Even if there are no accidents there is always a couple of slow spots that last about 5 minutes. Also in Oshkosh is an outlet mall. It is right across the road from the aviation museum. It has been 10 years since I have be to the museum but they had a flight simulator. It spun you 6 directions based on your moving the joy stick. Back then it was $5 for about 5 minutes. My son was about 12-14 and he had a blast. I dropped $20-30 as I let him get back in line a few times.
You may find a few inexpensive (no chain/franchise) places in GB that don't require a 2 night stay. My wife and I stayed at one years ago but I can't recall their name right now.
It might be the Bay Motel
I am not sure. When I stayed there I had to call the hotel directly to make reservations. They did not affiliate with any of the hotel wholesalers like Expedia or Orbitz. I have not stayed there again because by the time I figure out my plans they are booked. One of the other members of the site told me about the hotel. I can't say if they are still a clean place or not.
Depending on if you stay in Green Bay or further south I can give you directions to some places to park that are free and show you how to get in and out of town the quickest way. When I first got season tickets hardly anyone parked in the area and no one took my route to or from the stadium. Now it is a lot more congested but it is still better than the way most people go.
As for what tickets to get- I recommend an early season game.
First the weather is warmer and you will not have the cold weather gear needed. I had 5 layers on yesterday including stuff my son wore in Afghanistan. I wasn't cold but I was not not uncomfortably warm either. The roads will be in better condition. They do a great job of keeping the roads clear but being from down home (My wife's family is from TN) you don't often drive in 3-4 inches of snow. Why take the chance of ruining a fun trip?
Second you are less likely to have the game flexed on you to another time. You are going to be more or less locked in to a certain travel schedule and I can not tell you how inconvenient it will be if they move the game even 3 hours later little alone from noon to a night game.
If you do get a cheaper room you will have a little extra cash for a second night. That is the best way to take in all the sights. You can easily spend several hours in the Packer Hall. You will certainly want to look in the Pro Shop but it is going to be pricy for most items. There is a local sports apparel shop near the stadium that is a little more reasonably priced. Another reason for an early season game is you will still have plenty of daylight when the game is over. Even noon games late in the season will be getting toward sunset by 3:30 or 4. It is more likely to be overcast and only compound the feeling of night coming on.
I enjoyed just walking around the outside of the stadium and seeing some of the sights. I didn't look this year but in the past they have painted a new message on one or two of the fences north of the stadium. That is easier to do when it is warmer or on a Saturday before the game. Same for the Donald Driver #80 statue. It use to be outside the old Packer HoF but it has been moved to another area.
Zero is going to tell you to have lunch or dinner at HuHot. We had a great time when we went there.
As it gets closer we can talk some more. If you get the game that I have tickets to maybe will will have a chance to meet up.
Something else to consider is getting your tickets on the street. It is rather a big gamble but After kickoff any tickets still raining will be sold at a discounted price. It is a long way to go to take the gamble but it is an option.