To find a quality Ukulele, play the instrument to check the sound. Play a couple of whole songs the way you are accustomed. Then play each note on each string, starting with an open string, then playing each fret on each string. Listen for buzzing sounds that might indicate cracks in the body or a warped neck.
Study the body for cracks, the bridge to see if it is lifting off the body, the neck to see if it is separating from the body. Look very closely at the fretboard under the first few frets to see how deeply worn they are.
Choose tuning mechanisms of one of two types: right-angle gear drive, or adjustable friction (with a screw or something to prevent the peg from slipping).
Smell the hole in the body to see if it is moldy; if it is excessive due to wetness, the internal construction glue might come apart.