Bath Fan Exhaust Location

I have a 1st floor bathroom with shower in a cape cod with no exhaust fan. I am remodeling the bathroom and plan to install a fan/light unit.

Three options as no path to roof is viable:
1) Center of room with the exhaust vent over the bathroom window (Preferred). Window will not be open when fan is run.

2) Split over the shower rod. Half in main room and half over shower (Visually not my preference) with the exhaust vent just off to side of window

3) Directly over the shower with vent away from all windows. (I also do not prefer this as the fan will not be as convenient for removing odors, water issues, and do not want air moving over self in the shower...ceiling ht only 7.5')

Also do you recommend the traditional hood vent with flapper or the flat style with the 3-4 tabs that open and close? Live in Northern NY.

Thank you!

In a cape the ceiling joists are the attic floor joists and normally run front to back. So if the bathroom is on the front or rear exterior wall, it should not be a problem to put the fan where you want it and run the vent hose in the joist space. From there you can go out the wall or into the attic then to a ridge or gable vent.

I think placement option #1 makes the most sense; 7.5' is still pretty high, which means the steam from the shower can escape into the middle of the room where the fan would be. I am not sure of what the electrical code would require in your area, but mine would require the fan to be on a GFCI circuit if you went with installation #2 or #3.

As far as vents go, I prefer the look of the flat vents for side wall installations like yours, and the closed flaps keep bugs out.