..I think you're both blind. It's right there after the factory gets blown up by Julia.
After this cutscene, I'm assuming your team has a bunch of level 15's, maybe one or two level 16's, or if you've overdone it, perhaps a level 18-19 starter? If you feel confident about taking on Julia, keep reading! After all this hoopla, I think it's about time to take on the first gym, don't you agree?
From the factory, head south and follow the tracks, then head east when the tracks split. From where the lady is sitting on a few grass patches, head south and then east towards the big building. (You can't really miss it, it's decorated with pink ribbons..)