Hi Robonaut. Good question. My two cents:

The degree of danger depends on four things:

1. The type of solar event you consider. There is the 'normal' solar wind, which you may regard as baseline solar weather. From time to time, this wind gets supplanted with stronger events such as solar flares or coronal mass ejections.

2. Regardless of the event, danger rapidly decreases with increased distance from the Sun. This is because incident radiation follows an inverse square law. It drops off in proportion to distance from the Sun, squared.

3. Some types of solar output can be directional. Coronal mass ejections are one. If you're not in it's path, you'll obviously be ok.

4. Planetary magnetic fields play a very important role. Magnetospheres tend to collect and concentrate whatever radiation is out there. The Earth's magnetosphere, and consequent geo-magnetic storms, raise the risk in the near-earth environment.

So- the outer planets. You have a greater distance from the Sun (2), but they all have magnetospheres (4). Jupiter has the largest one by far. On top of this, Jupiter, together with it's moon Io, also produces it's own radiation. On balance, adding all this up, the Jovian environment is very dangerous.

Please note: This may not be entirely accurate. I'm no expert.