Good to see the thread still going. Lots of good ideas and suggestions in here! I know there's a ton of other compost type posts around the forums as well... but the "how far from the coop" - I'm not sure if it was addressed in other threads. Thanks for the thoughts, everyone that's contributed!
My coop still isn't complete... and now we've got snow in Upstate NY, so everything's at a bit of a stand still at the moment. That said, I did get my compost pile started near the coop. I've been making it a habit to put just a LITTLE bit of food in, and kind of digging in a little to place it toward the center and always bury it with shavings or leaves (we have PLENTY of leaves in this very deciduous area... oh my, there's "natural" compost piles everywhere honestly). Despite the fact that there's TONS of raccoons, skunks, crows, and dear around... no one seems to have disturbed the pile at all! This is good news to me!

I think it'll be ok to give the chickens a decent amount of "leftovers" and toss the rest into the compost as long as I follow this method!
I saw some ideas about freezing fruits and veggies in water for cool summer treats. Although, it sounded like most comments indicated people's chickens weren't very interested in pecking at frozen water and left the treats alone until the ice melted. I do like the idea though of freezing scraps. I already freeze bread heels and take them out to make breadcrumbs on the fly. There's no reason I can't toss another container in the freezer for chicken approved food scraps.
This weather needs to hurry up and get better again though! My chicks are creating a dusty mess in the laundry room... I'll miss their chirps though when I'm getting my morning coffee from the kitchen next to the laundry room! Already starting to hear a few clucks in there. I'm surprised my daughter hasn't suggested that we just let them stay in the cage inside like parakeets.