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The red spot is only part of the weather system. Regarding traveling there it would be pretty unpleasant for humans (as well as electrical equipment) as you need to shielding against Jupiter's intense radiation belts. On top of that if you were able to float around the cloud tops you would weight nearly 3 times as much!

I know, I saw a detailed info-graphic of the radiation belts there and on Saturn and how spacecraft avoid them when possible.

I seem to remember even some of the inner moons were deemed too dangerous to travel to. The magnetic field of Jupiter is many order's of magnitude stronger than earth's and there are a lot of high energy charged particles flying about. For this reason I think our first human trips would be to either Europa or Callisto.