Of the stars that can be seen with the naked eye, what are the distributions of each type? For example, how many are main sequence? how many are Super Red giants/white dwarfs/neutron stars...etc. What's the distribution by mass and distance?
I can have a stab at estimating the Neutron star population, and perhaps suggest how to do the others.
Now as far as I'm aware there aren't any Neutron stars you can actually see with the naked eye as there cold dead stars and we mostly observe them as pulsars in the radio band. But anyway, this article estimates we can observe objects up to "a little over 4000 light years away, " so lets use that.
Now the way to do this is to find a database, for pulsars there is the excellent ATNF Pulsar Catalouge. The joy of this site it it allows you to enter a condition.
So we ask it for names of pulsars with the condition
You can repeat this exercise if you can find similar online catalouges for the other objects your interested in, I'm afraid I only know about Pulsars.