This piece evokes the exotic imagery popular in American parlor music during the early 1900s. It uses flowing, wide-spread broken chords to depict its titular tropical theme.
The main technical hurdle is executing the arpeggios evenly across the keyboard.
Comparable difficulty and character — good candidates for what to learn next.
'Neath Hawaiian Skies is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 3.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of 'Neath Hawaiian Skies lasts about 3.5 minutes.
'Neath Hawaiian Skies is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Cathedral Voices by Charles Arthur Rawlings, 'Neath Swinging Roses by Albert William Ketèlbey, Berceuse, H.8d by Frank Bridge — see the full similar-pieces list on this page.