You are in wonderful, warm zone 9, so the list of tropical plants you can grow in your side yard is long and diverse. For big, bold beauties, try banana, ginger (both Costus and Hedychium), Brunfelsia, Clerodendrum, Caesalpinia, Dombeya, night-blooming cereus (Epiphyllum), and Brugmansia. You can also grow Jasmine, Gardenia, Wrightia, Chinese lanterns (Abutilon), Bauhinia, Cestrum, Iochroma, Justicia, shrimp plant (Pachystachys), and Rothmannia. Tropical vines you can grow include Hoya, Stephanotis (my personal favorite), Wisteria, and passion flower. The mulch you mixed into the soil can improve the soil tilth in both the clay and the sandy spots. Generous amounts of compost would be an excellent soil amendment prior to planting.