Traffic is not as bad as people make it out to be, unless you show up just before the game, try to park in the stadium lots, and then try to leave immediately.
If you show up early to tailgate (which you absolutely should), traffic won’t be an issue before the game. If you arrive close to kickoff, traffic can add 20-30 minutes to the end of your trip (i.e. on Route 1). Note that on game days the breakdown lane on Route 1 is open for driving. A lot of people don’t take advantage of this, so you can often skip a lot of traffic by staying to the far right lane. However, don’t try to use backroads to bypass the traffic: police block off access to the side roads on game day to all non-residents, so the only approach to Gillette is on Route 1. At the end of the game you have 2 good options to avoid sitting around for a long time getting out of the parking lot: tailgate again for an hour or two, or leave from one of the private lots. To do the second, park in one of the private business lots about a mile before the stadium. When you leave you’ll get in the lane that’s been reversed in direction, and you’ll be in front of all the merging that goes on to leave the parking lot, saving you more than enough time to make up for the walk. You will have to use Route 1 to get to the stadium regardless of whether you are coming the from the north or south.
There are a lot of options for parking. The stadium lots are the closest to the game, and cost $40 per car. They also take the longest to leave due to traffic. There are about 17500 stadium spots, with about half located across Route 1 from the stadium. These lots open 4 hours before the game. You do not need your ticket to park in the stadium lots (or any of the private lots, obviously).
In addition to the stadiums lots, all the businesses along Route 1 near the stadium offer parking on game days. The price at these lots varies depending on proximity to the stadium, but is in the range of $25-50 (yes, the last private lots just before the stadium lots cost more than the stadium lots). The main advantage of these lots is that it can let you avoid traffic, but being out in front of most of the merging. They also can be cheaper, depending how far you walk. Finally, you get access to the services of the business while parked (for instance you can eat McDonald’s or Chinese food or go the liquor store while tailgating). The downside is that you have to walk further to get to and from the game (plus they are smaller so tailgates aren’t as much part of a massive party).
Similar to driving, you can take a bus to the game. Rally Bus is a company that books travel buses for groups. On their site you can search by team for whichever game you are interested in attending & purchase spots on the bus by the seat. Each team/city has designated pick-up locations (Rally Points). The bus eliminates the hassle of driving, parking and navigating for those who aren’t from the area or those who want to drink. You can eat and drink on the buses while heading to the game. The buses park in one of the Gillette lots & arrives about 3 hours prior to the kickoff allowing plenty of time to tailgate (you may bring some tailgating items on the bus), then departs the game 45 minutes after the end of the game taking you back to the “Rally Point” the bus departed from before the game. Prices vary (depending on game and number of people on the bus) but seem to be in the $30-$50 range per person. At least 25 people must book a specific bus for it to be confirmed. You will still need to get to and from the Rally Point.
There is a train that runs to Patriots games, from both Boston and Providence. While it does not offer a lot of options, it might be better depending on your specific situation. The train will cost $20 dollars per person. If you are going alone, this can be cheaper than parking costs (or equivalent if you’re going as a pair). The train will take at least an hour and 5 minutes to get from South Station (or Providence) to Gillette (the section of the track that is the Gillette spur requires the train to go very slowly). You won’t get there early enough to tailgate or anything; you’ll have to go straight in once you get there. The train is scheduled to get there about an hour before kickoff, but it can get behind schedule. It will take the same amount of time to travel back after the game, but the train won’t leave for a while, as it needs to let people board (officially this is 30 minutes after the conclusion of the game). Expect it to take up to 1 hour and 45 minutes after the game ends to get back to the city. You’ll want to head straight back to the train when the game ends. If you are going alone or with just one other person, don’t want to tailgate, and are going to be right along one of the two routes (see the previously linked website for specific stops), the train might be a better option for you. Buy your tickets in advance to make sure you get one of the ~1500 spots.
Where to stay:
If you are coming from out of town, you may want to spend the night to avoid all the travel in one day (or turn it into a whole weekend trip). There are two main questions you will need to answer to decide where to stay: What do you want to do besides the game? How much are you willing to spend?
If you want to make an entire weekend trip out of it, you will probably want to get a hotel in either Boston or Providence. This will give you a lot of options for things to do on Saturday, and on gameday you can travel to it via the train or car. The downside to this is that the hotel prices can be pretty high if you go downtown. You can lower this cost for Boston if you stay somewhere further out and take the T in to the city (perhaps something like Quincy since it puts you closer to Gillette). This option is also closer to the airports (Logan in Boston or T.F. Green in Providence), which can be helpful if you are flying to the game.
If you are really only interested in the game, stay closer to Foxborough. This does limit your options for other things to do (the best thing to do in that area on Saturday would be to go to Patriot Place and check out the bars, restaurants, movie theater, bowling alley, and Patriots Hall of Fame). However, this will cut down on travel time to the game, and a lot of hotels in the area will run a shuttle to the game so you don’t even need to worry about driving. Prices in this area are normally lower, but on a gameday they will go up.
If you want to spend $500+ a night you can stay at the Renaissance at Patriot Place. This is literally closer to the stadium than some of the parking lots and is a very nice, upscale hotel. You have great access to the amenities at Patriot Place, but the downside for this option is pretty obvious: it is super expensive.