I was a single mom of twins, so I started going out with them alone... immediately. I found that people were willing to jump through hoops to help with twins, if I needed it, twins being SUCH an anamoly
I took them all over. We went to the mall, we went to the grocery store, we went for walks, we visited family. It's just a matter of having a "can do" attitude, in my opinion. If they started to melt down, well, I'd either finish what I was doing and leave, or just go with it until I could leave.
I actually found it WAY easier to go out when they were little and non-mobile than when they got older. Oy, when they were about 18mos-2.5yo they were RUNNERS FOR THE STREET, and I barely took them out by myself for months. So please enjoy the infant time when you can take them anywhere, anytime.