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

The simple answer is that the average galaxy spacing is around a few megaparsecs, while the biggest galaxies are around 0.1 megaparsecs in size. So the average spacing is somewhere in the range of 10 - 100 times the size of the biggest galaxies. The peas I had for lunch today were (at a guess - I didn't measure them!) 5mm in diameter so the interpea spacing would be 5 - 50cm, or between 8 and 8,000 per cubic metre.

But this is a very misleading statistic. Galaxies are not distributed uniformly, but instead are grouped into clusters, which are themselves grouped into superclusters. Also galaxies vary enormously in size, with dwarf galaxies around a thousand times smaller than the biggest galaxies.

I would resist the temptation to assign any significance to my figures above. However there is a take home message i.e. galaxies are much, much, much closer relative to their size than stars are. That's why galaxy collisions are quite frequent while stellar collisions are rare to the point of non-existance.

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:

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

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.