I sort of think you wouldn't see any stations or fellow ships unless you specifically aimed for those; space is big enough that a random encounter would be unlikely. No particular need for lanes, either: the ships would need to avoid each other, yes, but normally they'd be in no particular risk of coming to within (naked-eye) visual range of each other to begin with.
To truly appreciate the planets, I'd probably fly past them at distances ranging from a few thousand to perhaps ten thousand kilometers, plus of course the approaches and departures. That wouldn't yet count as "buzzing" them and entering densely inhabited orbits, but I'd see a lot of detail with naked eye. I'd deliberately steer past all the planets that lay even coarsely in line at the time, even if that meant serpentining quite a lot: the loss in overall travel time or fuel expenditure would probably be minimal. Perhaps a stroll past Venus plus all the outer planets in the approximate direction beyond Venus at that particular time. No point in going out of the plane of the system until I'd visited at least one of the outer gas giants...
Flying (slowly) through the rings of Saturn would be a thrill - but perhaps forbidden for the massed effect of thousands of starships opting for the stunt and disturbing the wonder of nature...? Skimming through the upper atmosphere of Jupiter or Saturn would be less likely to be regulated.
Timo Saloniemi