Guess I'm obliged to opine on this one.
I too have hiked at the Giant literally hundreds of times. It's very easy to craft a route that will cover more than 10 miles and roughly 2,500 vertical feet AND see few other people, all within a park that's only about two and a half miles in length. For those who have been there, a favorite jaunt of mine is to start at the back end, take the blue trail to the other end, the white trail back to where I started, the orange trail to the other end, and then the purple trail back once more to where I started. That's about 11.5 miles.
It's true that the tower trail sees probably 80% of the foot traffic in the park, but it's not a road - at least not for cars, though it is wide and smooth.
There are all kinds of neat things off-trail - caves, holes in the ground, great views, bizarre rockwork, etc. Most of the time you'd never dream you're five miles from downtown New Haven.
You really can't go wrong no matter which trail combination you take, as each one has its points of interest and even challenges. I've kind of gotten to the point where I ignore trails and just go from point to point, which, if you know the terrain, is not always easy and sometimes impossible. I guess in the 30s Sleeping Giant was one of the first serious rock climbing areas in the east, as you can read about in Forest and Crag.
And contrary to a post above, there are usually trail maps available at both the main entrance as well as the one at the east end of the park.