Pumping and breastfeeding in a public place is not for everyone. Thankfully, our culture has become more accepting of breastfeeding mothers and there are plenty of products out there that make the process convenient and discrete.
One of the best places to pump, for me, was in the car. It was a very productive use of time when we were going somewhere. It’s not easy and needs some getting used to but definitely doable. I would suggest getting a car transformer or adapter and keep tissues handy (always remember the water!).
If you don’t feel comfortable feeding/pumping in a public place, ask a manager to see if they can accommodate. Most people are very nice and supportive. Also, you might not even know it, but some public venues have already thought about the trouble you might face and made arrangements. When we went to the Philadelphia Flower Show, there was a little pod there specifically designed for breastfeeding/pumping. Sometimes, all you need to do is ask.