Nope, not everywhere! I have to go to too many places that aren't pet-friendly, like work and class. If I am out shopping or running a lot of errands, he stays home. If I have to run just a couple of errands (getting gas, going to the bank), he usually comes with me.
I do take him to tons of pet-friendly places: parks, pet stores, events, friend/family's houses. Usually he walks; occasionally I'll use a bag/carrier.
I am very lucky to have my brother willing to "babysit" Levi while I'm gone. He's rarely left alone for more than a few hours per day. He is happy to be able to go places with me, but he is also perfectly fine to stay home by himself for a bit.