It was a pleasure speaking with you today on our helpline.  You have a warm season grass, it could be Bahia, I can't tell without a sample.  Warm season grasses will green up when the weather warms and turn brown when the first frost hits. Your neighbor's tall fescue will be green in the spring, fall and milder winter as it is a cool season grass and normally would go dormant and turn brown in the summer when the heat kicks in.  We keep our fescue lawns green in the summer by artificially irrigating them.  If you are not going to irrigate your lawn, I would suggest keeping the lower maintenance warm season grass and replacing as much of the lawn with trees and planting beds as possible.

Azaleas and Hydrangeas may not be a good choice in the full western sun as they will need lots of supplemental water and tend to burn. Azaleas tend to like part shade and hydrangeas, while they can be situated in full sun, need protection from afternoon sun. Other choices can be found in this guide at:
https://www.fws.gov/chesapeakebay/resources/native-plants.html