Für Elise is perhaps the most famous short piano piece in the canon, beloved for its simple yet evocative rondo theme. Its combination of elegance and charm has made it an essential staple of piano study.
The main technical challenge is managing the flowing arpeggiated accompaniment while shaping the expressive melody with a singing tone.
Comparable difficulty and character — good candidates for what to learn next.
Für Elise (WoO 59) is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 6.
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 Für Elise (WoO 59) lasts about 3 minutes.
Für Elise (WoO 59) 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 12 Variations on 'Menuet a la Vigano' by Ludwig van Beethoven, 10 National Airs with Variations by Ludwig van Beethoven, (Ländlerischer Tanz) by Ludwig van Beethoven — see the full similar-pieces list on this page.