NASA mission data is archived at a handful of NASA archives. If you do not know which archive a data set is in, then you can search the Master Catalog at the NASA Space Science Data Coordinated Archive (NSSDC).
The main astrophysics archives are:
HEASARC (High Energy Astrophysics Science Archive Research Center)
IRSA (Infrared Science Archives)
LAMBDA (Legacy Archive for Microwave Background Data Analysis)
and MAST (Mikulski Archive for Space Telescopes)
Planetary/Solar System Data are at the various Nodes of the PDS.
NSSDC holds data from many of the older missions that predate these archives.
New Horizons data is being archived at the Small Bodies Node of PDS. But, it usually takes several months for data to get into these archives. So, if you are looking for very current images, you have to rely on what the mission team has put up on its web site. That is at their discretion.