Some ideas for getting out of the house for free: story times at the library, Life and Science and History museums in Raleigh, and walking around the mall.

What worked best for me when it was just me and a toddler at home was to rotate the toys. I always kept a big box of toys hidden away and if my son seemed particularly clingy or I needed a break, I would pull something he hadn't seen in a while out of the box. That would usually keep his attention for at least a few minutes. When I took something out of the box, I replaced it with a different toy.

Have you checked this out? http://www.trianglemom2mom.com/content/triangle-free-family-fun-guide

Your daughter might be too young for some of them, but it's a starting point. I didn't stay home full-time with my daughter at that age, but I was part-time. We'd take a lot of walks around the neighborhood ... very leisurely strolls and she'd just pick up sticks and watch birds. It at least got us out of the house.