The park is a great idea, you will meet other moms/kids
Bring lots of sandbox toys
Water or sand table is endless fun at that age.
You dont need to buy a fancy pre-made one, I flipped a big plastic bin over for a table & put on it, a pitcher, buckets & cups & measuring spoons. HOURS of fun.
You can also fill a large, shallow bin with either sand or water and have sand toys or floating &sinking toys.
To take this inside on really awful days, use rice. It is fun to play in & easy to vacuum up!
Finger or body paint with pudding. (non toxic, fun & delicious - hoses right off.)
Sprinklers & sprinkler toys / bubbles / chalk
Unfortunately at that age, there will be few activities that hold the attention for a long time, so, just be ready with an arsenal of things.