Real Solar System (RSS) is the real stand-out if you're going all-in. It converts the entire star system into our own star system. It's typically run with Realism Overhaul, which is sometimes also paired with Realistic Progression 1, but it can be run on its own with a part scaler like
SMURFF (because stock parts are far too inefficient to handle real-world scales).
Otherwise, the two extensions to KSP's existing system I'm most fond of are the
Outer Planets Mod and
JNSQ. OPM is a straightforward extension of the system outward with analogues to Saturn, Uranus, Neptune, and Pluto, along with a smattering of major moons, building off the vanilla scale. JNSQ is also an extension of the system outward with different analogues to these planets and moons, but it also rescales the entire system to a size between vanilla and RSS for more appropriate performance and sizes for vanilla parts (which are too efficient for stock solar systems). I recommend OPM if you're going for a vanilla-like experience, and JNSQ if you're also looking for something a little harder than vanilla or if you want to build really full-scale rockets. Then again, my current vanilla-plus game is OPM with a
rescaler that's configured to scale it up to approximately JNSQ size, so you can always configure as you wish.
Going out even further, if you have something like
KSP Interstellar and/or Nertea's
Near and
Far Future mods installed and are really looking to stretch your wings, there are handful of extrasolar systems to choose from. I cannot say much on this front as I've never gone for the extrasolar options, but
Galaxies Unbound appears to be current to the latest version.
I should note that while I provided links for your perusal, you may also benefit from looking on CKAN if you actually wish to try any of these. RSS/RO/RP-1 in particular is tricky to install manually due to the scale of its changes, and the team there strongly recommends using CKAN to install the components in the right order. The others or RSS alone can be installed manually more easily, so it's not actually critical. Also, some of them (JNSQ for sure, last I checked) simply aren't available on CKAN.