Not sure what you already know about tuning, but......one trick is I just use the tuner (or the piano) to tune the low E, then tune the rest of the strings to the low E, then check the low E again with the tuner when I get done tuning. I've noticed what you said, when I tune each string to the tuner, it's never really "perfect" according to the tuner.....so I tune the guitar to itself you might say, after getting the low E right. If the guitar sounds in tune with itself, and the low E matches all the rest of the instruments, then the guitar will sound in tune with the song.
If you play and sustain a low E on the piano, and play the low E string while the piano is sustaining, you can hear if they are in tune because the pitch will oscillate a little bit if it's off. Deliberately detune the E string - but do it slowly - and you will hear the speed of the oscillations increase as it gets more out of tune. When you bring the string back into tune with the piano note, the oscillation speed will become slower and slower until it stops oscillating completely. That is the point where the guitar string is in tune with the piano. Also works for tuning it to another guitar, play one low E string and tune yours to it while listening for this oscillation.
Also works for tuning the guitar to itself.
Works with perfect 4ths and perfect 5ths. I dont do 5th fret tuning like most guitarists. I play the low E and the second fret on the A string (two notes) this makes a perfect 5th (E and B). If you slowly detune the A string, you can hear the same oscillation in the sound of the perfect 5th. The speed of the oscillation will increase as the B (A string) becomes more and more out of tune. When you tune the string back to where it was, the speed of the oscillation will decrease, and it will stop completely when the E and the B form a perfect 5th. Then the interval is in tune. Repeat for the A string + E (2nd fret of the D string) pair.
For the G string I simply play the D string and the G string open, as a perfect 4th. Tune the G string until the oscillation stops.
For the B string I use another perfect 4th, by playing the A (2nd fret G string) and the D (3rd fret B string). Detune and retune the B string until the oscillation of the perfect 4th stops.
Same thing for the high E, play the B string and the E string open and detune/retune the E string until the perfect 4th oscillation stops.
Then play a bar chord or something to check the guitar. You may have to play a few minutes then repeat this process once or twice. The strings will change tension as you tune the first time, and they will warm up as you play which also means they will go flat as they warm up. It may take a few minutes and a couple of tunings to get it "stabilized"......