I've used a lot of different 35mm cameras over the years. Obviously, cameras with traditional layouts look and feel substantially different from modern ones. Your N80 is actually a good middle-of-the-road camera. It still has a dial, albeit for the selection of the operating mode, but it has wheels, so it is easy to use in manual mode once one becomes familiar with their placement and function. I have an N80 and it has become one of my favorite Nikons. I found an MB-16 battery pack for it, which gives the camera some extension and allows for the use of "AA" batteries, so one can fore-go the not-so-common CR123s. It isn't as robust as the F-series pro cameras, but if one takes reasonably good care of it, it should last a long time.
Since you already own a Nikon, it makes most sense for your second body to be a Nikon. That way they can share lenses. Assuming you don't have any G-series lenses, of course. There's nothing wrong with having another camera system (I own five different 35mm systems at present), but you'll wind up with some inevitable duplication.
I've used -- and own -- Nikons from the F to the F4, and several Nikkormats. Personally, I've never cared for having the shutter speed dial concentric to the lens mount, so I've never been a big fan of the Nikkormat. As for ergonomics of the F-series, with each subsequent model, ergonomics got better. The F is, for me, somewhat awkward to use. The F2 is simply great -- a perfect example of a "traditional" camera. While the F's corners are sharp and angular, the F2's are softened and rounded. It feels really good in the hand. Nikon took things a step further with the F3. Its ergos are even nicer. Plus, the camera is substantially lighter than the F2, although it's just as robust. The F4 takes things to a much higher level. It has retained all the knobs and levers and switches one would expect to find on a pro-level camera, but with the MB-21 battery pack, it has become a big camera with its high-speed integral motor drive. However, its ergonomics are so good that the added bulk and weight is not a burden. If anything, it feels very solid in ones hand. So, if you want to go with an F-series as your second (or first?) camera, which to use? Well, I'd say whichever you like the feel and layout the best with. They're all great, durable cameras.
You mentioned the Canon F-1. My personal favorite is the original F-1 (second version though), but the New F-1 is also one great camera. It has a better motor drive option and offers some exposure automation that the original does not (shutter and aperture priority AE depending on options). Both are very traditional cameras in terms of control layout and overall feel. If you wanted to open yourself up to a second system using cameras that are good in manual mode, these are two of the best.