Congrats on your first OC. I felt somewhat self-conscious my first time, too, but I was surprised by how quickly that went away. After five or six times it became normal for me, and I suspect your self-consciousness will fade soon as well.
Most places you probably patronize regularly are going to be good places: Meijer, Home Depot, gas stations, restaurants. But like Q said, you need a CPL to carry in places with liquor licenses, which are most grocery stores, gas stations, and restaurants, so keep that in mind.