As Super Bowl 51 winners, the New England Patriots will have the opportunity to host the first game of the year next season. Typically, NBC carries it on the Thursday before the rest of the regular season begins.
The Falcons are probably the best game there. The Panthers would be the NFC rep from the 2016 Super Bowl. The Texans have a great defense and JJ Watt, who I am told enjoys the spotlight. Those are the only three games that could compete with the Chiefs.
Based purely on football, the best opponents would be Atlanta and then Kansas City. Based on everything else the NFL bases it on, the Falcons probably make the most sense.