In P.N. Elrod’s Bloodlist, it’s Chicago, 1936. Jack Fleming wakes up on the shore, with no memory of how he got there. As he staggers toward the road, he’s deliberately hit by a car; suffering no ill effects, he easily subdues the driver—despite taking a bullet in the back in the process. Trying to figure out what’s happened, he realizes: 1) he has a number of terrible, half-healed wounds, including a bullet mark in his chest; 2) his heart isn’t beating; and 3) his reflection doesn’t appear in the rear-view mirror.
As the cover copy suggests, one of the benefits of becoming a vampire is being able to solve your own murder.
It’s kind of fun reading about Jack using his powers for investigation and revenge, though one might cynically suspect that the departures from, and adherences to, traditional vampiric powers were chosen to make the investigation easy. He also picks up an entertaining sidekick early on. The plot, though, basically consists of the two of them getting beat up, knifed, and shot, until eventually a location and sufficient pain jog Jack’s memory and he remembers just how he got all those wounds, which is not a cheery way to end a book.
I’ll look for more of these, but in the library or used (besides, they’re really short).