The "size" (Schwarzschild radius) of a black hole is directly proportional to its mass. The figure of merit that has to be considered, in order to resolve any spatial detail, is the angular diameter of the black hole as viewed from Earth. This will scale as $M/d$, where $d$ is the distance.
My understanding is that the black hole in the centre of M87 and Sgr A* at the centre of our Galaxy are the two black holes with the largest value of $M/d$.
Sgr A* : $M/d \sim 4\times 10^{6}/8 = 5\times 10^{5}\ M_{\odot}$/kpc;
M87 : $\ \ $ $M/d \sim 6\times 10^{9}/16\times 10^3 = 3.8\times 10^5\ M_{\odot}$/kpc.
Your suggested alternatives.
Andromeda : $M/d \sim 2\times 10^8/8\times 10^2 = 2.5\times 10^5\ M_{\odot}$/kpc;
Triangulum: doesn't have a known central supermassive black hole?
So Andromeda is not a crazy target. It's angular size is only 2/3 that of M87. However, another issue is how many of the 8 telescopes in the network can view Andromeda at any one time? It's impossible for the South Pole (as was M87), but also not visible for very long from Chile, so there is a reduced baseline coverage.
A further crucial argument is to consider the timescale of variability in the object. In order to co-add images you need be sure the image is stable on long enough timescales. But the timescale of variability for accretion-illumination in a black hole is proportional to its mass (see Why was M87 targeted for the Event Horizon Telescope instead of Sagittarius A*?) and this timescale is only about 2 minutes for Sgr A* and and hour os so for Andromeda. This makes less massive black holes harder to image with this interferometric technique.
These two quotes seem like they contradict each other. Which one is correct?
They do contradict. Please be aware that comments cannot be downvoted so they often serve as a haven for content that an author suspects would be severely downvoted.
One thing that both the answer and the comment share is that the horizon is a lightlike surface. If a flash of light occurs below your feet then it reaches your feet before it reaches your head. It does not reach both at the same time. The event horizon, being also lightlike, follows that same pattern of motion locally.
This is true in every local inertial frame. The temporal ordering of lightlike separated events is frame invariant. So any nearby inertial observer, regardless of their relative velocity, will agree that the horizon reaches your feet first and then your head.
Best Answer
Of course they targeted Sgr A* as well.
I think though that this is a more difficult target to get good images of.
The black hole is about 1500 times less massive than in M87, but is about 2000 times closer. So the angular scale of the event horizons should be similar. However Sgr A* is a fairly dormant black hole and may not be illuminated so well, and there is more scattering material between us and it than in M87.
A bigger problem may be variability timescales$^{\dagger}$. The black hole in M87 is light days across, so images can be combined across several days of observing. Sgr A* is light minutes across, so rapid variability could be a problem.
The penultimate paragraph of the initial Event Horizon Telescope paper says:
$\dagger$ The accretion flow into a black hole is turbulent and variable. However, the shortest timescale upon which significant changes can take place across the source is the timescale for light (the fastest possible means of communication) to travel across or around it. Because the material close to the black hole is moving relativistically, we do expect things to vary on these kinds of timescales. The photon sphere of a black hole is approximately $6GM/c^2$ across, meaning a shortest timescale of variability is about $6GM/c^3$. In more obvious units: $$ \tau \sim 30 \left(\frac{M}{10^6 M_{\odot}}\right)\ \ {\rm seconds}.$$ i.e. We might expect variability in the image on timescales of 30 seconds multiplied by the black hole mass in units of millions of solar masses. This is 2 minutes for Sgr A* and a much longer 2.25 days for the M87 black hole.
EDIT: 12th May. And here it is, an image reconstruction, published by the Event Horizon Telescope consortium (see here) for the black hole at the centre of the Milky Way. The image is a time-averaged composite reconstructed using a novel dynamical imaging process for about 10 hours of VLBI data.