As pointed out above, one thing I liked in TOS was that we were way, way out on the edge of explored space, at least most of the time. In TNG, they go zipping back to earth for any old reason, and I don't recall much exploration or new contacts (at least in comparing TOS' three seasons to TNG's seven).
The original series never returned to present-day Earth for reasons explained in The Making of Star Trek
and elsewhere. But all of the original-cast feature films (four of which preceded TNG) included at least one scene on Earth. TNG had to follow suit and become more Earth-centric; the reasons for avoiding it weren't relevant anymore.
But yes, I did enjoy that aspect of the original show. For some reason I've never been able to put my finger on, the most "remote"-seeming episode for me has always been "Return to Tomorrow" - and it's not just the captain's log saying how far out they are, or his "risk is our business" speech. It's something more subtle, involving the new George Duning music and (for all I know) the color of the planet.