You already got great advice, and I don't know how much mine will count since I don't mind being a little more dressed up (as long as I'm not too overdressed). I'll just add:
-A walk in the park?
Are we talking a leisurely stroll, including long sit-downs on park benches or picnic blankets... or a bona-fide fitness walk? If the former, then my Me-too flats have proven to be 8-hour flats, and as a plus, they are easy to kick off for relaxing under a tree. If the latter, then yes, a fashion sneaker or even a downright fitness sneaker (in which case, I'm probably opting for gear I can sweat it). It depends on expected MPH. My DH, while taller than me, walks slower than me. I cannot get him to speed up to my normal power-walk gait to save my life. He'd rather lope along.
-Supporting hubby at an endurance bicycle race?
*Probably* I'd just wear gear, since at these events that's what most people do, and hubby would probably give me a huge gross sweaty hug afterwards, ruining my fancier clothes! However, if I am really just standing on sidelines, and there is a celebratory gathering afterwards (like at a restaurant) I may dress up a bit - sandals or flats, clams, nicer knit top. Simple.
-Hiking/Camping? Yeah, I know it's camping, but I still don't want to look like a total slob.
Absolutely GEAR for this. You don't want to get sweat, campfire smoke and OFF smell all over your good clothes. Don't do it!! Wear machine washable jeans, top, sturdy sneakers. If you are combining camping with other dressed-up activities, then of course, bring along nicer clothing to wear for the other activities. But wear gear for the camping/hiking parts.
-Backyard BBQ?
Clams or skirt, knit top, cardi or jean jacket (if it gets nippy), nicer flat shoes (sandals or flats). Maybe a day dress, if I know the other guests will wear one. Leave purse in the car, so you don't have to juggle it with your picnic plate.