Go through the main entrance to Avondale Park, and take the path between the ball fields and the little lake. (Stop to say hello to the ducks along the way. They get amused when I shake my tail feathers along with them.) When you get to the base of the hill, you'll find King's Spring.
It's a nice spot to dip your toes in the water. King's Spring was an often-used spot in the 1800s. Many people stopped here to water themselves and their horses- though some of the ones who wore blue were shot at by people who wore gray. (I can, with some confidence, say there's a MUCH lower chance of being fired upon here in this modern age, no matter what colour you're wearing.)
The spring once flowed down the center of Spring Street (see what they did there?), which is now 41st. That is neither here nor there, as you will be off-roading.
I was first drawn up the hill by the two stone 'reviewing stands', where one can watch the people in the park below. I kept going past them- and you will, too.