Congratulations on your new daughter! At 3 months old, babies really don't need to "hang out on their own" very much. That's sort of an American culture myth. They're still very new and need lots of parent interaction. She is just learning about her world, so some days she may not make a whole lot of eye contact, just because there is so much going on around her to look at. My son is 3 1/2 months as well, and I interact with him ALL day long. A day might look like: feeding in the morning, cuddling, then I'll make a little pallet on the floor with a blanket and his little stuffed animals while I vacuum, etc. Then the rest of the day we interact basically all throughout the day - more feeding and cuddling of course, I'll go for a walk and show him flowers, hold out his little hand to touch leaves, stuff like that. Back at home I read books to him and let him look at the pictures, we also do lots of baby exercises - I'll hold him under the shoulders to stand and let him practice "walking," or I'll sit in front of him and make a game out of helping him sit up or have tummy time. We also play peek-a-boo, then we'll lie down and take naps together. I also always make good eye contact every time I change his diaper and talk and sing to him. When my husband gets home, he holds him and talks to him while I make dinner. Don't believe any of the books that tell you you'll spoil her with too much contact, or that we need to teach babies some independence. Little infants need lots and lots of parent attention and support. Give her a little time to get used to her new world, and I bet she'll reward you with lots of eye contact and smiles very soon!!