In my last games I tried to play specially through common quarters but they still don’t make any sense. The reason is the fact that all quarters have the biggest income from adjacency, while common quarters annihilate it.
Solution could be very simple. Now we have many civics that buff common quarters, but the bonus they give is so small, that it feels meaningless. So I think all civics that buff common quarters shall give bonus for adjacency. For example, instead +1/+1 money/science on common quarter, it shall give +1/+1 money science per adjacent quarter. So shall do other bonuses.
Speaking of garrisons, I propose they should work in the same way they work now, but start exploiting nearby tiles. Therefore, they will be placed in not the worst tiles, but in good strategic places without loosing the terrain bonus. The same I would be applied to religious districts making them more valuable