I have a mid-sized Land's End backpack that has non-stretchy mesh side pockets for water bottles and the Universal cups fit perfectly in there. I've found that I can even carry the cup there with beverage still in it as long as it isn't completely full and I keep the back pack level (don't lean over or anything). I learned this at
HHN when you weren't supposed to take drinks into the houses but I hadn't finished by the time I got to the door.
This backpack has padded straps and the padded interior "pocket" meant to hold a laptop, but it fits in the free locker if I kind of fold it over. If there is a lot of stuff in it, however, another family member has to also get a locker so we can empty some of the larger things into the second locker.
We've also found that you can fit a popcorn bucket into a free locker if you take the lid off and bend it slightly.
I'm not a light park-traveler--I like to carry everything with me that I may need-- but I won't pay for a locker.