I used to hate to spend time by myself. I think I'd have been considered an extrovert once upon a time, but that has changed as I've gotten older. I've become more comfortable in my own presence and now I cherish time to myself.
I'm a stay at home mom, so I don't get a lot of that time to myself thing. Even my morning yoga is done in the living room with my hubby present and sometimes at least one kid. I often will finish the physical part and then retire to my bedroom for some quiet contemplation or meditation. I also write with others in the room most of the time. I plug in my headphones and turn on my writing station on Pandora and just try to block out my environment. The kids will come over to get my attention and up will go my finger in that universal signal for 1 minute please - they've learned to wait patiently while I finish my thought - then I give them my attention. It's the same for my artwork. I have a corner of the living room set up with my drafting table with all my art supplies and that's where I sit to do my sketching, zentangling, or quilling. One side affect of this is that I end up sharing my passions with my family - I think the kids seeing me engaged in what I love is important. It may not be a perfect system, but it works for us.
One thing I've come to really prioritize for myself is me time. My darling hubby is a champ at facilitating this for me. When he gets home from work he usually gives me some time to go to our bedroom and just be by myself. I usually read or meditate, but the being by myself thing is key. If it's been a particularly trying day - I'll get cranky if I'm interrupted, but most of the time the family is very respectful of that time to myself. I've really come to need it - that me time.