Jlui has some great suggestions on geographic pairings. Up in North Dallas, courses aren't really as convenient to one another. If someone here can give you a current status on Audobon, I'd recommend pairing it with Harry Meyers in Rockwall -- it's probably the most convenient 18 near HM and it's a great course when the grass has been mowed (and a hellacious course when the grass is high). The other pairing to consider is the new Paschall Park in Mesquite; I haven't played it yet, but have heard some good things about it -- and we need some more reviews for that course on here, so it would be great to have your thoughts. The final option there is B.B.Owens, which is a decent little 18 -- fairly open, but some fun shots and just enough elevation to make it interesting; BBO also often has a lot of wind, which is a good thing, as it adds a lot of interest and challenge to the course.
Beyond that, the other Dallas courses are spread so far apart it's hard to conveniently hit two courses in a day. Of the remaining courses, my favorites are Alex Clark in McKinney and Lake Park in Lewisville -- but those are probably at least 45-60 minutes away from one another, though I think they've finished Hwy-121 enough that you could cut through on that and not be too bad off. Only problem is that traffic in Dallas on weekdays can be as bad as anywhere in the nation, so you want to avoid some of those areas like the plague in rush hour. So if I were you, I wouldn't end your trip with those two -- catch them together on one of your midday trips. Play Lewisville first, then head out to McKinney, and that should flow better from a traffic standpoint than the other way around.
IMHO, the best courses in the area are Harry Meyers, Veterans, Z-Boaz and the Cedar Hill courses. So just plan to save one of those four for your last day to end on a high note. The prettiest and most relaxing of those courses are the Cedar Hill courses -- they are not huge bomber courses, but are both very shady with pretty decent signage and some unique holes. Don't expect Cedar Hill to destroy you, but expect it to be the most enjoyable place in the city to spend a summer day golfing.
For sheer challenge, Z-Boaz and Harry Meyers are at the top, depending on where the pins are in the ground. Harry Meyers from the long tees can be demoralizing, depending on your skill level -- it's more fun from the short tees, and a better tournament course from the longs.
So quick recap, if I were planning your trip, and trying to balance courses for endurance, variety, challenge, etc... I'd plan it like this:
Day 1: Arcadia, North Park (warm-up day)
Day 2: Bicentennial, Z-Boaz (long day of challenging golf)
Day 3: Lake Lewisville Park, Alex Clark (rest-up)
Day 4: Veterans, Bear Creek
Day 5: TBD, Harry Meyers
Day 6: Coyote and Beaver at Cedar Hill
If you want to sneak a few extra courses in there, there are some fun 9-hole courses in the DFW area. I don't know exactly where you are staying, but if Fritz Park in Irving is on your way somewhere, it's got some great holes -- all flat, but relaxing and open under lots of large trees. Also, on the Lake Park/Alex Clark Day, I'd plan to stop between the two at Bill Allen Memorial Park in The Colony -- it's a short nine hole with several water hazards that is very picturesque. A couple of stellar holes, and some fun short ones. It's worth playing and won't tire you out. It's also next to a Hererra's, which is some of the best Tex/Mex you can get in the DFW area. Neither Bill Allen or Alex Clark will wear you out, so the Tex/Mex won't kill your game.
Also, when you finish off at Cedar Hill on day 6, coming back from there, a few miles away at Sam's Pizza, they have the best New York-style pizza I know of in the Metroplex. It's a great place to rest and replenish your carbs/salt after a long week of disc golf. The last time I played Cedar Hill, my brother and I got in four rounds of all 36 holes and finished off the day at Sam's and it was wonderful.
Have a great time with your brother -- some great golf to be had there.