Jovian magnetosphere is extremely active and stretches nearly all the way to Saturn. It is indeed in volume the second largest continuous structure in the Solar System, right after the heliosphere. Jupiter's radiation in the radio frequencies is in fact so strong, you can tune in and listen to it between frequencies of other radio stations on AM/FM radio receivers. This is a bit of oversimplification, since what you'd hear is a composition of various other celestial bodies emitting radio frequencies (pulsars, the Sun,...), and also Earth's atmospheric charge, but the Jupiter is particularly loud and accounts for the large portion of musical notes in this Cosmic opera.
This radiation in the radio frequencies could potentially be tapped into and converted to electricity. Alternatively, oscillations in magnetic fields as Io orbits Jupiter cause a huge Alfvén wave electric current carried by magnetized ring of ionized gas by between Io and Jupiter. The power of this field is estimated to be around two trillion watts and is the biggest DC electrical circuit in the Solar system known to man. So that are two renewable sources - the electric current, and the highly charged plasma itself.
Io is also highly active itself, constantly being at the mercy of the the enormous gravitational pull of Jupiter. Due to it, it's geologically highly active, and is known to produce volcanic eruptions that eject large amounts of sulfur dioxide gas into space. As such, it is a strong source of plasma. There is also a potential to tap into the geothermal wells and convert that power to electrical current.
There are also other opportunities around Saturn. One idea (admittedly pretty wild, but why not?) that comes to mind is taking advantage of the electrostatic charge of the Saturn's rings. In theory, it's as huge of a collector as they come. Also, the Saturn moon jets, that were detected by the Cassini Solstice Mission carry a potentially huge amount of kinetic, thermal and electric energy in the form of charged plasma.
Thinking farther, all the way to Pluto, tidal forces created by gravitational interaction with Charon as they orbit each other (I can't really say Charon alone orbits Pluto, since they're tidally locked to the other and Pluto orbits a point outside itself) might be strong enough to produce "cryo-geysers" of ammonia hydrates and water crystals on the surface of Charon, as suggested by observations of the Gemini Observatory. And, of course, we already know of other methods of producing electricity by effects of tidal forces - i.e. tidal power.
So these are all sources that can be considered as sustainable. There are all kinds of other opportunities to collect energy in sustainable ways around gas giants, their moons, or even their interaction as they orbit each other. We just need to learn how, and develop technology to convert and/or store all this energy to our liking and needs.
