If you haven't had a chance to visit MOBOT, get over there and quick! :)
On Wednesdays and Saturdays before noon, the botanical garden is FREE to St Louis City and County residents. Not only is the garden free, but also the Children's Garden! You will need to give your zip code when you first arrive. Parking is always free. The garden is open every day of the year except Christmas.
Other ways to save on admission: Active duty military receive a two-for-one admission if you are going at a non-free time, or are not a St Louis resident. There is also a $1 discount if you show a valid Metro fare (ticket, transfer, or pass).
Tip: Do NOT wait outside in the ticket lines! You can purchase/pick up tickets at the counter inside the main entrance as well. Many people stop outside and stand in line when there is no waiting inside! Even if you are getting in free or have passes, you will need to stop at the ticket booths and pick up tickets which you will then show on your way into the garden. Be sure to pick up a map at the ticket booths as well, or ask for one.
It is a wonderful place to be, regardless of how hot it is, since there is plenty of shade. You can wander around and take pictures, or go climb a treehouse, or sit next to a relaxing lily pond.
Keep in mind that picnicking is not allowed in the garden, so if you want to make a day of it you can leave your picnic lunch in the car and go eat in Tower Grove Park (directly south of the entrance to MOBOT). I believe that the Garden does not allow in/out privileges, but I'm checking on that and will update this as soon as I know.