2 of 3 added 18 characters in body

A couple of maps for you, both taken from the Star Trek: Star Charts book:

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As you can see, the border between Alpha and Beta quadrants passes through the Solar System, effectively splitting the UFP territory in two almost equal parts. It is roughly a situation equivalent to the Greenwich meridian

So, to answer your question: TOS, TNG, DS9 and ENT (and now DIS too) take place equally both on the Alpha and the Beta quadrants.