How far apart are galaxies on average? If galaxies were the size of peas, how many would be in a cubic meter?

Simple question requires a simple answer! There are 9,900,000 light years on average between galaxies.

How we come to that number: The average distance between galaxies is a few megaparsecs. A megaparsec is 1 million parsecs and there are roughly 3.3 light years to a parsec, so that means there are on average, sticking with threes, we'll say a few equals 3, 9,900,000 light years between galaxies in a galaxy cluster that is.

Assuming (in 2018) we have about two trillion galaxies in an observable universe 46.5 billion light years in radius, we can compute the average volume per galaxy and take the cube root of that volume to obtain a flawed but useful notion of average distance between galaxies:

$$sqrt[3]{frac{ frac{4 pi}{3} (4.65cdot10^{10})^3}{2cdot10^{12}}} approx 5,949,391 approx text{six million light years}$$

While this is a notional average, it is not the typical distance between nearest-neighbor galaxies. It would be akin to computing the average distance between grains of sand on the beach by assuming that the grains of sand are spread uniformly over the whole earth. (Bear with me as the illustration may be useful for comparison.)

Assuming $7.5 cdot 10^{18}$ grains of sand on an earth with a radius of $6,378$ kilometers, the square root of the average area occupied by a grain of sand is:

$$sqrt{frac{4 pi (6.378 cdot 10^6)^2}{7.5 cdot 10^{18}}} approx 0.00826 approx text{about a centimeter}$$

...yielding about a centimeter of separation between grains of sand on the beach, which is as misleading as the notion of six million light years between galaxies.

So, the best way to answer your question might be to look at our own Local Group of galaxies. Our Local Group has two major players, Andromeda (M31) and the Milky Way, which are separated by about 2.5 million light years. Around each of these is a clump of much smaller orbiting satellite galaxies. For the Milky Way, our satellite galaxies (a few dozen of them) vary in distance from our galactic center from about $50,000$ light years to over a million light years.

Finally, to answer your question informally, one might say that judging by our own neighborhood, galactic nearest neighbors tend to be on the order of about $100,000$ light years apart, but galaxies tend to travel in clusters that are separated by tens to hundreds of times that much.

For study and visualization of 3D structure and distribution of 4673 galaxies less than 200 Mpc from Milky Way, we (Douglas and I) have developed an open source web simulation with many tools to aid analysis: riteshsingh.github.io/galaxies/

The code is open source under the MIT license at github.com/RiteshSingh/galaxies.

The associated publication is available here: academic.oup.com/astrogeo/article/61/4/4.42/5873800 and papers.ssrn.com/sol3/papers.cfm?abstract_id=3668727.