I'd say the baby care centers were my favorite places for changing diapers, but sometimes the diaper needs to be changed ASAP and you aren't going to tote the kid across the park to a baby care center. Then I did the old out of the way stroller diaper change. I always carry plastic bags to tie the stinky diaper up in and chuck it into a bathroom trash can. Of course, with diaper changes, you have wipes handy, so I used one of those and some sanitizer for my hands. Wet diapers? Standing in a stall is a perfect solution for those!
The changing tables in the bathrooms are OK (many are made of stainless steel), but sometimes there is a line for them, sometimes they aren't the right size, and sometimes it is just more convenient to change the kid in the comfort and privacy of their own stroller.