Here are some options, I'm going to throw in a college game (Saturday) too, to make this a full USA football experience.
Week 2:
Saturday: Clemson @ Florida State
drive ~ 7 hours south
Sunday: Buffalo @ Miami
drive ~ 5.5 hours back north
Monday: Pittsburgh @ Jacksonville
Week 3:
Saturday: Iowa State @ Texas
drive ~ 3 hours
Sunday: Washington @ Houston
drive ~ 6 hours
Monday: Atlanta @ New Orleans
Week 4:
Saturday: Northwestern @ Penn State
drive ~ 4.5 hours
Sunday: Indianapolis @ NY Jets
drive ~ 2 hours
Monday: Green Bay @ Philadelphia
Week 7:
Saturday: Colorado @ Oklahoma
drive ~ 7 hours
Sunday: Jacksonville @ Houston
drive ~ 4.5 hours
Monday: NY Giants @ Dallas
Week 8:
Saturday: Illinois @ Wisconsin
drive ~ 2.5 hours
Sunday: Arizona @ Green Bay
drive ~ 5 hours
Monday: New England @ Minnesota
Week 10:
Saturday: Georgia @ Auburn
drive ~ 2.5 hours
Sunday: Cleveland @ Atlanta
drive ~ 4 hours
Monday: Tampa Bay @ Carolina
*Bonus: Can see UTEP at UAB on Friday night (~ 2 hours b/w Birmingham and Auburn)
Week 11:
Saturday: Western Michigan @ Florida State or Western Carolina @ Floriday (neither tickle my fancy, Western Carolina isn't even Div. 1A)
drive ~ 4 hours
Sunday: Washington @ Tampa Bay
drive ~ 3.5 hours
Monday: NY Giants @ Jacksonville
Week 13:
Saturday: Louisville @ Pittsburgh
Sunday: Tampa Bay @ Pittsburgh
drive ~ 5 hours
Monday: Carolina @ Philadelphia
My advice: Go with the week 10 trip as it provides the best combo of warm weather, good games, low travel.
Of course if I was planning a trip I would wait for the NHL sched too
I recently had family move down to Houston, so I may go for a Texans game, plus I want badly to see a Texas A & M game (fans stand all game, wear purple, the tradition of the 12th man).