I wanted to create a scene where two god-like characters are talking or fighting on a planet or fragment of planet to which they've teleported that's about to be obliterated by a black hole.

The characters are effectively gods so heat and gravity won't affect them too much. I wanted the black hole and stars being engulfed to fill the sky.

At what distance could a planet still have some surface to stand on as it orbits the black hole before turning completely into dust?

For this, we need to know two things: how close you can get to the center of mass of the black hole before the tidal forces tear you apart, and the radius of the event horizon.

The first is determined by the Roche limit: $d = R_m (2 M_M/M_m)^{1/3}$, where $R_m$ is the radius of the smaller object, $M_M$ is the mass of the larger object, and $M_m$ is the mass of the smaller object. This assumes certain simplified conditions, so in practice, you may want to add a margin of error.

The second is defined by the Schwarzschild radius: $r_s = 2GM/c^2$, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

Assuming a planet and supermassive black hole roughly comparable to Earth and Sagittarius A* (the one at the center of the Milky Way), respectively:

$d approx 2.65 times 10^6 m$

$r_s approx 1.27 times 10^{10} m$

$d < r_s$

So as long as you aren't actually inside the black hole, the planet isn't going to break apart from the tidal forces. Supermassive black holes are fun that way. (Do not try this with a regular size black hole.)

Orbits at that distance aren't stable, though. You'll need an orbital radius of at least $3 r_s$ if you want it to last.

Of course, your orbital velocity at that distance is around 0.4c, and you're constantly accelerating in the direction of the black hole, so you'll probably get some weird relativistic effects (I don't know enough general relativity to tell you what they'd be, though). And there's probably no way the planet will be able to keep an atmosphere. And if the black hole is still actively feeding, there will be probably be horrible levels of gamma radiation; I'd recommend an inactive black hole if you want to keep the temperature somewhat reasonable. But as long as you're outside the event horizon, it'll be an intact uninhabitable, superaccelerated, and possibly molten ball of iron.

You want to know how close your planet would get to a supermassive black hole.

• The vicinity of a super massive black hole as the one at the centre of our galaxy is an extremley hot, turbulent, and magneticaly charged zone, it would also compass jets of charged particles, gamma radiation and (very hot) dust.




• The Black hole itself is thought to be in the order of 100,000 solar masses, the theoretical maximum limit being thought to be in the region of 50,000,000,000 (50 billion
  solar masses) for an ultramassive black hole.

The Accretion disk:

• This is proportional to the size of black hole, some are speculated to be thin and comparativley cool, just like a planetary disk. The one at the centre of the galaxy is wide, thick and hot.




• Velikhov-Chandrasekhar instability (or Balbus-Hawley instability) means that differential magnetic field densities in the disk make the material towards the centre of the disk move faster than that on the outside - more than would be accounted for by different orbital velocities at these distances. This signifies that there is huge friction surrounding huge vortices of superheated turbulent material constantly swirling in a dance around the centre.




• The plasma of the disk, highly electricaly conductive, carries currents of inconcievable magnitude, sporadically discharging to nearby regions of different charge in colossal lightning bolts as the maelstrom whirls about it's centre, ejecting a jet of energy from the poles of the black hole.

How much energy is released in an accretion disk?

Accretion process can convert about 10 percent to over 40 percent of
the mass of an object into energy as compared to around 0.7 percent
for nuclear fusion processes.

• That is, it (mass for mass) converts nearly 60 times more of the matter going into it than the sun converts it's own mass into free energy - heat, light, gamma rays, the energy of the jet being ejected from the poles.

The Polar Jets:

These radiate energy in a concentrated beam on the axis of rotation of the disk. In extreme cases, the total energy radiated by the disk and by the polar jets can equal thousands of times the total radiant light from all the stars in the rest of the galaxy combined. They can be seen shining brightly from across the farthest reaches of the universe that can be seen.

Relativistic beaming of the jet emission results in strong and rapid
variability of the [jet's] brightness.

Conclusion:

On approaching the accretion disk:

• The planet would approach the disk boundry and melt, quickly being pulled apart by the magnetic fields and dissolve in the swirling motion of the disk in a blaze of gas plasma.

On approaching the polar jet:

• The planet entering the jet would be almost instantly vapourised and be carried away with the jet's (near light-speed) motion.

The Planet wouldn't get near the black hole itself.

_References:

https://phys.org/news/2018-02-ultramassive-black-holes-far-off-galaxies.html
https://en.wikipedia.org/wiki/Accretion_disk#Magnetic_fields_and_jets
https://en.wikipedia.org/wiki/Magnetorotational_instability
https://en.wikipedia.org/wiki/Supermassive_black_hole
https://en.wikipedia.org/wiki/Quasar