Jazz bass pickup height
 

What are your preferred pickup heights for a Fender Jazz bass?

Here's some info directly from Fender which I find useful. Remember, these are guidelines so your playing style and tone preference may dictate a deviation from this:

PICKUPS

Setting pickups too high can cause a number of unusual occurrences. Depress strings at last fret. Using a 6" (150 mm) ruler, measure the distance from the bottom of the first and fourth strings to top of the pole piece. A good rule of thumb is that the distance should be greatest at the fourth-string neck pickup position and closest at the first-string bridge pickup position. Follow the measurement guidelines from the chart below as starting points. The distance will vary according to the amount of magnetic pull from the pickup.

Note: Larger string gauges need wider vibrational allowances. If you have a five-string bass or are using heavier-gauge strings, your measurements must be increased accordingly.
Bass Side Treble Side
Vintage style 8/64" (3.6 mm) 6/64" (2.4 mm)
Noiseless™ Series 8/64" (3.6 mm) 6/64" (2.4 mm)
Standard "J" or "P" 7/64" (2.8 mm) 5/64" (2 mm)
Special Design Humbuckers 7/64" (2.8 mm) 5/64" (2 mm)