[pretysmitty]

So NAD+ has a N with an unfilled octect in a conjugated system. I can see how if it were to gain 2 more electrons, it would then be an aromatic compound and more stable, so it's an electrophile. But why is it a particularly attractive compound for redox? Surely there are other nitrogen compounds that can participate in redox and are more easily synthesized. Or is it just random chance that evolution decided on this compound? I find that hard to believe, but I don't really see why another compound can't be used.

[Babcock_Hall]

What makes you think that the nitrogen that is within the ring of the nicotinamide system has an unfilled octet?  Which form, NAD or NADH, is aromatic? 

With respect to your title, "good" can mean many things.  Biochemists often classify oxidizing agents on the basis of half-cell reduction potentials at the biochemical standard state, in other words on the basis of E°' values.  For NAD the value is -0.320 volts.  Does that make it a relatively weak  or a relatively strong oxidant?  However, kinetics are also important to consider, and reactions of NAD/NADH are almost always catalyzed by enzymes (NAD can be an electrophile in some addition reactions that are not catalyzed by enzymes).  Therefore, one might ask what about NAD or NADH might be advantageous from this perspective.

[pretysmitty]

This is probably a basic misunderstanding, but the nitrogen in the ring in NAD+ has a positive charge so I assumed it was unfilled. Is it actually because it's electrons are delocalized via resonance?

Given that NAD+'s E° is more negative than most organic compounds, I would say that it is a (relatively) strong oxidizing agent. Can we related its strength in terms of potential to its structure? Could I go as far to say that strong electrophiles can be strong oxidizing agents due to their affinity for electrons?

[Babcock_Hall]

A more negative value of E°' is associated with a greater tendency for the oxidized form to take electrons in a redox process, and a greater tendency for the reduced form to give electrons in a redox process.  For example there is another redox pair, namely ubiquinone and ubiquinol, and E°' is roughly +0.06 for the reduction of ubiquinone (I have seen similar but not identical values, depending on the source of information, and there is no need to worry about small differences at this point).  Which is the stronger oxidant, NAD or ubiquinone?  Which is the stronger reductant, NADH or ubiquinol?

Many nitrogen-containing species have a formal charge of +1 on nitrogen yet all atoms have filled shells, for example NH₄⁺.  I suggest looking at the structures of NAD and NADH, preferably with the electron pairs drawn out explicitly.  Wikipedia's drawings do not show the lone pairs, but they can be added in.  In both structures the nitrogen has a full octet. What is different about the nitrogen in one versus the other?  What is different about the two six-membered rings?
https://en.wikipedia.org/wiki/Nicotinamide_adenine_dinucleotide

I think that it is probably better to keep separate the concepts of electrophilicity and ability to act as an oxidant.  I have a couple of reasons for saying so, one of which is the nucleophilicity and electrophilicity are defined in kinetic terms (how quickly something reacts), whereas E°' is a thermodynamic quantity.

[Babcock_Hall]

I see nothing wrong in looking at characteristics such as aromaticity or formal charge when studying the structures of NAD, ubiquinone, FAD, or other biological oxidants.  On the contrary, biochemistry students should spend more time than they generally do getting to know these structures.  However, most of these biological oxidants have several structural differences versus the other oxidants.  Therefore, attributing a difference in reduction potential to a single structural difference would not be advisable IMO.

[Babcock_Hall]

A more negative value of E°' is associated with a greater tendency for the oxidized form to take electrons in a redox process, and a greater tendency for the reduced form to give electrons in a redox process. 

I see that I mistyped something.  I should have said, A more negative value of E°' is associated with a weaker tendency for the oxidized form to take electrons in a redox process..."