Can you bring dogs around besides the dog runs?

Yes

I seen people bring their dogs in the picnic area and walking around the park leashed.

I saw a sign that said dogs must be leashed. Plenty of people doing that. I'm pretty sure dogs cannot go into the zoo area. Have fun! Nice park!!

I seen someone had a dog with them but I feel not a good idea cause you are in a zoo n u never know reactions, but I would call n ask for a better advice.