Piano Piece?

I like the Bach C major prelude and fugue. It's the very first one when I open up my book of ps&fs so I don't even have to go looking for it.
Haydn's D major sonata is great.
Also maybe dedicate some time at the beginning of your lesson to a chopin etude: his revolutionary etude is quite popular. Just 5-10 minutes a day learning a few measures really pays off.
Debussy's 1st arabesque is very nice also.
Maybe you could even do some Rachmaninoff or Scriabin's easier works (of course their easy works are advanced). I like Rachmaninoff's op32 no12 and of course there's his famous op3 no2 prelude or even his flight of the buumblebee (personally this piece drives me nuts but I like cziffra's version ; ] )
Beethovens tempest sonata would be really nice too.
I'm not sure what style or level of advanced you'll looking for exactly so I tried to give a bit of a mixture- I'd probably say the pieces are around the grade 7-10 mark.

I think the river flows in you is a beautiful song for the piano. It may be too easy for what you're looking for though.

There are fabulous selection in the Songs Without Words book by Mendelssohn. Advanced but approachable. I once learned a Spanish Dance by Granados that was sooo much fun. Difficult yet approachable. It was fast but stylish and graceful. It was from the Granados book. I also suggest Debussy's Mazurka. Short but highly appealing and just as approachable. His Prelude in F from the Debussy book is a bit longer than the Mazurka but I think you'd like it. Ethereal and dreamy but lavish. Good luck, hope this helps.

Easy yet advanced-
Maybe some of the more advanced waltzes (Op. 18, Op. 34 No. 2)? If you really don't have time, try a longer mazurka.
Brahms rhapsody Op. 72 No. 2 might work too.
or perhaps a Fauré barcarolle.
Some early Beethoven sonatas may do, though you may want to select certain movements since you don't have much time.
I don't think Bach is a wise choice if you don't have much time for practice. It will probably result in a mechanical performance. I think it's OK to hear late classical or romantic pieces with limited musicality - if you do all your notes, dynamics, tempo, etc., right, there will inherently be some appeal to it. Half-done Bach, however, is, to me, no better than Philip Glass...

The heart asks pleasure first-Michael Nyman
Falling away-Elijah Bossenbroek
Una mattina-Ludovico Einaudi