  Extremely large telescopes (ELTs) present an unparalleled opportunity to
study the magnetism, atmospheric dynamics, and chemistry of very low mass stars
(VLMs), brown dwarfs, and exoplanets. Instruments such as the Giant Magellan
Telescope - Consortium Large Earth Finder (GMT/GCLEF), the Thirty Meter
Telescope's Multi-Objective Diffraction-limited High-Resolution Infrared
Spectrograph (TMT/MODHIS), and the European Southern Observatory's Mid-Infrared
ELT Imager and Spectrograph (ELT/METIS) provide the spectral resolution and
signal-to-noise (S/N) necessary to Doppler image ultracool targets' surfaces
based on temporal spectral variations due to surface inhomogeneities. Using our
publicly-available code, $Imber$, developed and validated in Plummer & Wang
(2022), we evaluate these instruments' abilities to discern magnetic star spots
and cloud systems on a VLM star (TRAPPIST-1); two L/T transition ultracool
dwarfs (VHS J1256$-$1257 b and SIMP J0136+0933); and three exoplanets (Beta Pic
b and HR 8799 d and e). We find that TMT/MODHIS and ELT/METIS are suitable for
Doppler imaging the ultracool dwarfs and Beta Pic b over a single rotation.
Uncertainties for longitude and radius are typically $\lesssim 10^{\circ}$, and
latitude uncertainties range from $\sim 10^{\circ} \ \rm{to} \ 30^{\circ}$.
TRAPPIST-1's edge-on inclination and low $\upsilon \sin i$ provide a challenge
for all three instruments while GMT/GCLEF and the HR 8799 planets may require
observations over multiple rotations. We compare the spectroscopic technique,
photometry-only inference, and the combination of the two. We find combining
spectroscopic and photometric observations can lead to improved Bayesian
inference of surface inhomogeneities and offers insight into whether ultracool
atmospheres are dominated by spotted or banded features.
