>>810520More info on where, when, and how would give you better answers.
That said here's a few general things I can think of for being /out/ in general:
-water, bring a little more than you think and drink more than you want.
-snacks. In addition to eating meals, snack a lot. Being outside burns a ton of calories, and often times you might not even realize it. If you find yourself tired or angry, take a break and eat something.
-wool or polar-fleece jacket/sweater (if possible, don't sweat it if all you have is cotton). Even in the middle of summer, it gets cold at night. The wool/polar fleece is because it keeps you warm even if it's wet, unlike cotton. This leads me to my next point...
-a cotton bandanna. lots of uses. in the summer heat it's really nice to soak and then tie around the head, or have on the neck.
-duct tape (repairs, good for blisters if hiking)
-bug spray (bring a ton of it if youre going somewhere low and buggy)
-entertainment (deck of cards, book, instrument, small portable game)
-a hat. yes your fedora could work, or just a cap or anything to keep the sun off. Maybe sunglasses, maybe both, whatever makes you comfy.
If you are hiking, there are a few more things to consider.
-talc powder (gold bond) or vaseline or anti-chaffe stuff. This is a godsend when you need it, and life sucks without it. Your nuts will thank me.
-extra socks
-find two sticks for walking with
-do away with extravagances, try to pack lightly. It really matters for comfort and it's easier to realize you could've carried more than to realize you can't carry what you brought anymore. Don't pack your fears.
Above all else, trust your brother and coordinate with him on what you bring. Have fun, take pictures and tell us how it goes.