Liebestraum no. 3 is very well known, romantic, and pretty. Liszt Consolation no. 3 would be good too.
^ this
For generalization, 50% of Chopin's work for romantic melodies as well as recognition given that it's in every soundtrack featuring 'classical' music.
Specifics:
Liszt
-un sospiro (play it, say the name, then the translation: 'a sigh'. Then listen to all the girls sigh)
-harmonies du soir
Blumenfeld
-Etude pour le main gauche (show them you're 'talented' with your off-hand

)
Henselt
-Wiegenlied, op. 45 (then tell them it's a lullaby you plan to play to your children)
- One of the etudes from op. 2 with cheesy love based names in french, same 'strategy' as un sospiro
Alkan
- Assez Vivement, op. 38 no. 1 (not necessarily the most romantic, but since many romantic pieces are in minors, this is a nice happy change of pace that sounds much more impressive than it's difficulty)
Godowsky
-Chopin etude transcription #45 in E (from nouvelle etude no. 2 in A-flat)
Schubert
- Impromptu in G-flat, op. 90, no. 3
Rachmaninoff
-Piano transcription of his paganini variation no. 18
Lastly, any of these pieces will start a conversation. You still have to have personality... so leave the piano every now and then and socialize
