This place is magical. I really don't feel the need to expand on this statement too much. Go, just go! This is my only advice to you.
I suggest taking the tram ride if possible. This enables you to get a mini tour and see the lay of the land, it also provides shade on a hot day. We learned some really cool things about the Thai Pavilion we might not otherwise have learned if we didn't take the tram ride.
Family friendly and affordable fun; It's free to enter the gardens and $2.00 per person to enter the conservatory.
They suggest you make a donation, and so do I.
This is a Madison treasure, I hope to enjoy in all seasons!