I would like to build a bonsai bench in my backyard. Where is the best location for a bonsai bench?

Depend on the species you are putting on it.

Pines: Full sun exposure
Palmatums: Mid-day shade

Make sure it is not in a drafty area. And ideally a westernstorm should not hit it directly

Consider whether you want water shelter or not etc.

There will only be junipers on this bench. I've read that they will need full exposure and I've also read that they do better with morning sun and afternoon shade. Which, if either, would be best?

For me, junipers are in the sunniest spot I can provide, right next to the pines.