This is what the tree seedlings look like

 

this is what the seeds look like

 

Catalpas leaf out early in the spring, and by June have large white flowers. They are easily recognizable by their large heart-shaped leaves. By late July or early August the seed pods are visible; they are green at this time. After the leaves drop in the late fall the seed pods will be brown; they will hang on through winter and sometimes into the next year.  

I have left these descriptions vague so you will have the fun of finding the trees for yourself.

In Wilmington proper there are several nice trees. One of my favorites is at 18th N and West St. There is a very productive (lots of flowers and seed pods) on 19th by Bancroft Parkway. If you have sharp eyes you can spot several large trees between exits 2 & 4 on the New Jersey Turnpike; even at 65 mph the large heart-shaped leaves and hanging pods are immediately recognizable. Closer to home there is a large catalpa tucked in among the willows across from the entrance to Trees from Seeds; this one flowers early and has sparse seed pods; look for the old sofas and tires.

These seeds are very easy to grow. The pods should be gathered when they are brown, but before they split open. The seeds need to be held over the winter in a cold (ambient) location, and kept fairly dry. In the spring the pods should have split open to release about 100 or so small light seeds. The seeds just need to be placed about 1/4" deep in potting soil and kept moist; they usually germinate in about 3 weeks. I have always had a very high germination rate, nearly 100%.