Welcome to the forum!!
Tickets, as you know, are sold out on a season ticket basis. You would be purchasing your tickets from a season ticket holder, through websites like
Titletown Tickets,
Packer Fan Tours, or
Stubhub.
Those are the three I would recommend. Packer Fan Tours, and Titletown Tickets are both locally owned in Green Bay, and reputable. And Stubhub is another safe option as well.
As for pricing, tickets usually range anywhere from $85-$200 or more. The marquee match ups (Packers/Vikings, Packers/Cowboys, Packers/Bears, will always be more expensive; while home games against the Bills, Lions, and Niners, will be the cheapest.
As for when they tend to be cheapest, you will just have to check often, as the prices can and will fluctuate.
If you purchase any tickets, you will not receive them until after August 1st, as that is when they are mailed out to the season ticket holders.
Websites I do NOT recommend, are Ebay, and Craigslist. With Ebay, people tend to over bid on the tickets and you end up paying way more than they are worth. And with craigslist, you just never know what you are going to get. The websites I suggested, are safe, reputable, and they will NOT rip you off. I have used Titletown tickets the most, as they tend to have the cheapest prices.
As for hotels, I have tried a few different ones and have usually went with the
Bay Motel, as they give you the best deal, as far as price and quality. All the hotels in Green bay will have a two night minimum on Packer weekends. Usually the first two nights will be $100 or more, with any additional night being around $50+. One hotel I would not recommend would be the Road Starr Inn right across from Lambeau. It is over priced, and not very nice.
Or if you don't mind a 20 minute drive, you can stay in Appleton, which is about 25 miles from Green Bay, and the hotels are cheaper. I always stay in Green Bay because I like being close to everything.
Another thing you could try, is booking a hotel, and flight through websites like
www.orbitz.com. Sometimes you can get a good deal if you book both at the same time.
As for places to go in Green Bay (bars, restaurants, etc) you can't go wrong anywhere you go really. The burgers at Bentley's are absolutely outstanding, I will say that.
One thing you will want to do is the Lambeau Field Stadium tour. They do tours everyday except for game days, and you get to walk through the players tunnel, and onto the Frozen Tundra, as well as tour the luxury suites.
Sorry for the long winded response. I am sure there will be others that will have suggestions as well. Feel free to ask an other questions you may have. I hope you get to make the trip, and I am sure if you do, you will have a blast!