A follow on craft, redesigned for lower cost and incorporating lessons learned from Cassini, New Horizons, Dawn, Mars Reconnaissance Orbiter and sent to Uranus and another to Neptune would be a reasonable direction for continued outer solar system exploration.
For instance, the camera system; with Voyager we had pixels on the narrow angle camera around 4 arcseconds square. Very good for the time, and based on a design first used on Mariner 10 which was sent to Venus and Mercury. With Cassini, the pixels on it's best camera were around 3 arcseconds square, a nice bump, roughly the area of 2 pixels for each pixel Voyager had.
Then on New Horizons, the best camera had pixels ~1 arcsecond !!, so very nearly 16 pixels for every pixel Voyager had. This was needed since Pluto is so small, and the flyby speed was so great, a higher magnification allowed better pictures further out and for a longer time in which to gather them.
The ultimate in beyond earth resolution is the HiRISE camera on the Mars Recon Orbiter. It's pixels are ~ 0.2 arcseconds. equivalent which means the HiRISE camera can put ~400 pixels in each of Voyagers !!
(the ultimate, so far BTW, is the Hubble Space Telescope with 0.1 arcsecond pixels)
Now, keep in mind, the smaller the pixels your have, the more stringent the stability of the spaceprobe becomes. Additionally, to counteract that, you can add aperture to keep exposure times low. HiRISE, in use at Mars has quite strong sunlight for picture taking. New Horizons, OTOH, at Pluto had very dim sunlight available. Unfortunately, adding aperture to the camera system adds weight. The HiRISE system by itself masses more than all the instruments on New Horizons put together. So you see the tradeoffs that have to be made. HiRISE resolution at Neptune would be quite a trick, lofting that heavy of a camera (and it might even be heavier with even more aperture to counter the dim sunlight there) on a probe that will be relentlessly pared down for weight will be an enormous challenge.
Another challenge is orbit design. Cassini was fortunate to have Titan at Saturn to bend it's flight path. Titan is sufficiently massive that Cassini was able to change it's inclination around Saturn by up to ~10 degrees in a single flyby. Since the mass ratio at Jupiter for even Ganymede is so much smaller, the Galileo probe was essentially confined to equatorial orbits. Even maximum attempt at Ganymede to increase the inclination would only be a degree or 2, requiring a large number of flybys to 'crank' the orbit much to look at the polar regions. The same issue exists at Uranus, the moons just aren't massive enough to change inclination with. (they are large enough to allow deflections to direct a probe to each other, however)
A probe at Neptune will enjoy a similar capability that Cassini had with Titan, the mass of Triton is sufficient for 'cranking' the probes orbit out of it's orbital plane.
And al, of this (and much more) is fun to work with, but with out some serious $$$$ thrown at these projects, nothing much is going to happen for a very long time.
For instance, the camera system; with Voyager we had pixels on the narrow angle camera around 4 arcseconds square. Very good for the time, and based on a design first used on Mariner 10 which was sent to Venus and Mercury. With Cassini, the pixels on it's best camera were around 3 arcseconds square, a nice bump, roughly the area of 2 pixels for each pixel Voyager had.
Then on New Horizons, the best camera had pixels ~1 arcsecond !!, so very nearly 16 pixels for every pixel Voyager had. This was needed since Pluto is so small, and the flyby speed was so great, a higher magnification allowed better pictures further out and for a longer time in which to gather them.
The ultimate in beyond earth resolution is the HiRISE camera on the Mars Recon Orbiter. It's pixels are ~ 0.2 arcseconds. equivalent which means the HiRISE camera can put ~400 pixels in each of Voyagers !!
(the ultimate, so far BTW, is the Hubble Space Telescope with 0.1 arcsecond pixels)
Now, keep in mind, the smaller the pixels your have, the more stringent the stability of the spaceprobe becomes. Additionally, to counteract that, you can add aperture to keep exposure times low. HiRISE, in use at Mars has quite strong sunlight for picture taking. New Horizons, OTOH, at Pluto had very dim sunlight available. Unfortunately, adding aperture to the camera system adds weight. The HiRISE system by itself masses more than all the instruments on New Horizons put together. So you see the tradeoffs that have to be made. HiRISE resolution at Neptune would be quite a trick, lofting that heavy of a camera (and it might even be heavier with even more aperture to counter the dim sunlight there) on a probe that will be relentlessly pared down for weight will be an enormous challenge.
Another challenge is orbit design. Cassini was fortunate to have Titan at Saturn to bend it's flight path. Titan is sufficiently massive that Cassini was able to change it's inclination around Saturn by up to ~10 degrees in a single flyby. Since the mass ratio at Jupiter for even Ganymede is so much smaller, the Galileo probe was essentially confined to equatorial orbits. Even maximum attempt at Ganymede to increase the inclination would only be a degree or 2, requiring a large number of flybys to 'crank' the orbit much to look at the polar regions. The same issue exists at Uranus, the moons just aren't massive enough to change inclination with. (they are large enough to allow deflections to direct a probe to each other, however)
A probe at Neptune will enjoy a similar capability that Cassini had with Titan, the mass of Triton is sufficient for 'cranking' the probes orbit out of it's orbital plane.
And al, of this (and much more) is fun to work with, but with out some serious $$$$ thrown at these projects, nothing much is going to happen for a very long time.
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