Once you have to go up the fretboard for a particular note, see how long you can stay in the same position. When you hit a note which is outside the range of pitches available in that position, you'll move to a new position, but again, see how long you can stay in that position. To get more familiar with the fretboard, I practiced reading fiddle tunes, using a linearly tuned ukulele (forcing me to use notes on the 4th string, if I wanted to avoid excessive position shifting).
Also, when you have melodic scale runs, try to incorporate the 4th string, which is too often neglected when playing melodically. In any particular position, its pitches will overlap with the upper notes (in that position) on the second string and the lower notes on the first string.
There is a simple four-node, movable, cyclic fretboard pattern you can use to quickly find notes on the upper fretboard—and in fact, it's composed of the same string-to-string offset patterns that you use to tune an ukulele to itself using unisons and octaves:
From the 3rd or 4th strings, skip a string (to the 1st or 2nd, respectively) and go up three frets.
From the 2nd string, go to the neighboring 3rd string ("inside to inside") and up four frets.
From the 1st string, go to the 4th string ("outside to outside") and up two frets.
These offsets can be chained end to end to go higher and higher on the fretboard from any starting position (a note on the lower neck whose name you know), and you'll hit every note of the same name in "fretboard order". To see how this works, look at a fretboard map, pick any pitch name and follow the offsets up. It should take very little time to master this pattern. Once you locate notes in this pattern, you can see how they fit into your mental picture of the fretboard in that fretboard region, so that you can later find these notes by simple recall (and by direct association with the standard notation pitch locations).
For notes in the region just below the 12th fret, it can be faster to start at or above the 12th fret and walk the pattern down, but before trying that, first internalize the upward patterns. Though I now know my fretboard pretty well (at least for C and G tunings), I usually play using relative offsets and lose track of note and chord names; I find that using patterns like this "same-name zigzag" is usually faster and surer than relying on my recall of the fretboard.
As for chord/melody, that's another kettle of bees. There are strategies to greatly tame the "difficulty" of it, but it really helps to have done ear training in intervals first, so that you can distinguish which component of a chord a melody note maps to. If you can do this, predicting the location of the chord root (and even the shape of the desired chord) is pretty easy—though not so easy that I can describe it quickly here.
