I love Pinecrest Gardens because it not only has some beautiful trails, it also is very reasonable to visit. It's only $3 for adults and $2 for kids! Kids love this place because there is so much to see and do including a playground, petting zoo, Splash 'N Play, and of course, the botanical garden. It's open 9-5 in fall and winter and 9-6 the rest of the year. I would go on a Sunday because there is a free farmer's market outside of the garden. There is so much tasty, fresh food to take home or enjoy while at the gardens. It runs from 9 am - 2 pm every Sunday.
This is definitely a great, family friendly spot to enjoy a morning in Miami. They sometime do plays and shows in the evening, so check out their event calendar on their website for info.