Independent absolutely. I need "me time" so my boyfriend better find hobbies and activities to do so he isn't bothering me, texting me, or calling me to check and make sure I still love him. (My sister had a boyfriend like that.)
My boyfriend and I are pretty good together. We both do our own thing during the day and come home and have dinner and hang out together at night, but sometimes we do our own thing then too.
I like having a boyfriend that doesn't freak out when I spontaneously decide to go on a road trip with my friends. I like a boyfriend that doesn't mind if I'm gone for a week on vacation without him.