When I pour oil into the engine via the oil fill port that my oil filler cap seals off where does all that oil go initially?
On most vehicles, the oil goes into the sump (or oil pan) at bottom of the engine. The sump is where the oil pump pickup is located and where oil distribution starts during engine operation.
What parts get first dibs on the oil before gravity pulls it down to the pan.
If you are talking about after the oil is pumped through the engine by the oil pump, it depends on how the engine is engineered. Some manufacturers send oil to the cam shaft first while others send it out to the crank shaft main bearings first. The latter is called Priority Main Oiling. This ensures the bearings have appropriate amounts of lubrication during high engine speeds. Again, it's all in how the engine is designed as to what gets the oil first.
Are the oil filler ports always on the top of the engine?
No. They can be located just about anywhere near the top of the engine, or not on the engine at all. Having the oil filler cap on the valve cover is just a convenient place to have it. It's a broad surface where a filler cap can be placed. Here is an image of an older Small Block Chevrolet (SBC Gen I) engine. The filler for it was the black tube which stuck up from the center front of the engine (also doubled as a breather):
As stated, the filler cap doesn't even need to be on the engine. With a dry sump design, the filler cap is on a reservoir tank located separately from the engine. The engine has a scavenging pump which pulls all of the oil from the shallow oil pan sump and drops it into the reservoir. The main oil pump pulls oil from the reservoir tank and distributes it throughout the engine where needed. This is mainly used in high performance applications where there needs to be a constant feed of oil. In an engine with a typical sump, the oil may be forced away from oil pickup during hard acceleration, cornering, or braking.
Is there any particular reason other than maybe ease of access as well as avoiding spills and leaks, basically trying to maximally distance the port from the oil settling line?
I think you have it covered within the question. That's pretty much the reason.