of is entirely optional and usually omitted colloquially. The same goes with most other prepositions. However, in cases where there is potential ambiguity, it's advisable.
I enjoy the friendly atmosphere of StackExchange and my local Starbucks down the street.
Here one could interpret it as my enjoying the Starbucks itself, rather than its atmosphere. It would be more precise to write:
I enjoy the friendly atmosphere of StackExchange and of my local Starbucks down the street.
Or to adapt @ruakh's nice example,
children of Adam and Eve might be construed as "Adam's children and Eve".
Depending on your audience, it may not matter as common sense will guide their interpretation. For more complex thoughts, the choice may be important.
I called up an old friend, with whom I grew up in the great state of Arizona, and [with whom I] went fishing after lunch.