Dead on the Island
The first book in Bill Crider's "Truman Smith" PI series, it introduces private investigator Truman (Tru) Smith . Smith, a BOI (born on the island) returned to Galveston Island to try and find his missing sister. He has failed, and is painting houses to get by, running along the seawall when his weak knee lets him and reading Faulkner in his spare time (and also feeding Nameless, the cat who hangs around).
Smith is asked by his high school friend Dino to find Sharon Matthews, the daughter of one of the women who worked the whorehouses run by Dino's uncles when Galveston was wide open. He first thinks the girl ran away when she found out about her mother's past, but finding Sharon's boyfriend murdered, and then getting beat up outside a Houston nightclub, convinces him that there is more going on.
He must dig into his and Dino's past, and there will be more bloodshed before the story is told. Smith makes an interesting detective: wracked by guilt over the failure to find his sister, he's a bit adrift. Crider's "Sheriff Dan Rhodes" series is more successful (up to 16 or 17 books) but this one is well worth searching out also.