Only visited once, for a day, several years ago. I don't remember much, but I would say check out the Southernmost Point and I think Mallory Square. If I remember correctly, there was a guy who did a skit pretty much every day (according to others that 'knew' the area), and it was neat taking his picture along the water at sunset.
Not sure if you're driving there from southern Florida, but if you are, lots of photo opportunities along Route 1.
I hope someone comes along and provides better advice!
Definitely Mallory Square, also East Martello Towers on the other side of the island can be awesome, while not the physical sunset, the sky can light up with color. Fort Zach is another great place to take some fantastic sunsets.
I'll assume you know key west pretty well so I'll save myself from the other spots.
I'm a total newb but I remember hearing something about it being bad for the camera to have the sun in frame for too long with the aperture wide open. Maybe it doesn't apply as much to sunsets or i heard wrong. I found one article and can only repeat what it says. Aperture seems medium to high meaning closed, shutter speed a bit slow (for the high aperture), ISO very low and wide lens if you got it. Try a few settings. Best camera settings for sunsets (free photography cheat sheet) | TechRadar
Also another article suggests underexposing to get more color and has lots of tips. 30 Sunset photography tips