SuperGirl is usually Miss Bubbly Sunshine, but I'm sure she has times when she feels completely isolated. She really has very few peers on Earth; we're literally aliens to her... she literally has no friends with whom she can share herself without reservation.
I thought about that myself. Unlike her cousin Kal, she actually *remembers* Krypton. She's permanently trapped in a backward foreign country and that's before we consider the cheery thought of knowing that all her home, friends and family (besides Kal) are gone.