Are you getting a parking pass? If offered one, take it! You can get into and out of the stadium (and park right next to it) through the back gate on dedicated roads, which allows you to avoid all the traffic. You want Lot 5 if you have a parking pass. If you do not have a parking pass, if coming from the north (down Rte. 1 south) try Lot 33 which is a dirt lot pretty close to Gillette Stadium, but on the opposite side of Rte. 1. You can make a left turn out of the Lot at the end of the game onto Rte. 1 north. When leaving, stay in the left-most lane (which is actually a lane on the south side of Rte. 1 that they have go in the opposite direction at the end of the game) for the fastest "out". You're getting close on Rte. 1 south when you go through the last light before Gillette at North Street, where there is a McDonalds on the corner. Then it goes Liquor Store lot (also popular), dirt lot, little bridge (black rails) then the entrance to Lot 33 right after the little bridge. It's close to Lot 54 on the parking maps of Gillette stadium, but they don't show it on the official map. $60 to park last time I was there (outrageous I know). This lot has historically been an "easy out" after the game, but lately it hasn't been as good as in years past. It's pretty close to the stadium though and takes you right by the Pro Shop and Patriots Place when you go into the stadium.
If you are coming from the south, try the Pinebrook Office Park lot right after Rte. 140 joins Rte. 1 north. You are getting close when you see the state police barracks, then the entrance to Rte. 140, a Dunkin Donuts then some orange cones, which allow the folks getting on at Rte. 140 a dedicated lane for about 100 feet. The entrance to the Pinebrook Office Park lot is RIGHT AFTER the cones, so you have to get over quick (and perhaps suffer some honks). It's usually $40 to park, but I think they up it to $50 for the playoffs (also outrageous). Easy left turn out onto Rte. 1 south, and then onto Rt. 495 after the game. The only drawback is the distance from the stadium - about 1.3 miles. I will probably be here on game day.
Good luck and have fun! I am jealous of your "suite seats!"