Week 1: Green Bay Packers
Week 2: at New Orleans Saints
Week 3: at Carolina Panthers
Week 4: New York Giants
The Patriots preseason is filled with coaches that Bill Belichick respects and it seems very likely that the team will host joint practices with both the Packers and the Saints.
New England will benefit from an away-and-away with their NFC South opponents, and it wouldn't be surprising if the Patriots opted to host an extended road trip for the sake of team bonding, a la the 2014 midseason road trip from Green Bay to San Diego.
Week 4 is the annual Patriots vs Giants preseason slug fest, where Jimmy Garoppolo is going to shine and throw for 700 yards, eight touchdowns, and run for three more, probably. Regardless, Tom Brady won't be playing.
The preseason is an important time for teams to develop and it's a great opportunity for unheralded players to leave their mark. Without the preseason, there likely is no Malcolm Butler on the Patriots roster, so each snap is extremely important.