According to Memory Alpha, the Klingon capital is located in the Beta Quadrant, as is Vulcan, Andoria, and a number of other well-known planets.

So, as one example, much of Sins of the Father was set on Qo'noS, and hence in the Beta Quadrant. Similarly, a number of episodes were set on Vulcan, and The Aenar was set on Andoria.

From the fact that the Enterprise NX-01 visited both Andoria and Vulcan at least once, without apparently needing to travel any unusual distance to do so, we can even speculate that most of Enterprise was probably set in the Beta Quadrant. (This is supported by Star Trek: Star Charts.)

Support for this interpretation in primary canon is limited.

According to Memory Alpha, the Klingon capital is located in the Beta Quadrant, as is Vulcan, Andoria, and a number of other well-known planets.

So, as one example, much of Sins of the Father was set on Qo'noS, and hence in the Beta Quadrant. Similarly, a number of episodes were set on Vulcan, and The Aenar was set on Andoria.

From the fact that the Enterprise NX-01 visited both Andoria and Vulcan at least once, without apparently needing to travel any unusual distance to do so, we can even speculate that most of Enterprise was probably set in the Beta Quadrant. (This is supported by Star Trek: Star Charts.)

Support for this interpretation in primary canon is limited.