Hi mjames,
The Sonatina in G major Anh. 5 1st movement by Beethoven is both accessible and has the pretty melody.
The Sonatina in A minor, Op. 94, No. 4 1st movement by Biehl is also very pretty and was going through my head all day one day.
The Sonatina in F major, Op. 168, No. 1 1st movement by Anton Diabelli is another "pretty" one.
These are not "sonata" movements but are both good stepping stones to more difficult movements and quite satisfying to learn and play. Since you say you have "sort of neglected" the classical era, I just thought I'd mention them.
"Real" sonata movements for your consideration:
1. Haydn's Sonata in F Major, Hob.XVI:9 Third movement: Scherzo
2. Beethoven's Sonata in G major, Op. 49, no. 2 1st movement (Grade 8 RCM)
3. "Moonlight" 1st movement. Popular, yes, but you don't mind, right.
These are "accessible", below grade 7 and pretty.
I hope that helps, Joe.