Since you mention "the city" I assume you mean the Central Business District? In which case the suggestions in Williamstown and St Kilda are a bit too far away.
To impress, you'd probably be looking for something a little upmarket, or a little unusual (e.g. not a sandwich bar, etc.)?
Bar Lourinha is great for Spanish tapas-style dishes, with a good wine selection by the glass (assuming a bottle is too much at lunch time). In a similar vein, you could try
Movida.
Yuu is a very stylish hidden-away Japanese place, which serves set lunches (i.e. no choice). The food at lunch is so-so, but the atmosphere is great if you are (or she is) into the whole wabi-sabi Japanese aesthetic. Bookings are essential.
Or try
Punch Lane, a modern-European wine bar, which has a good selection of food plates of various sizes.
The Press Club is absolutely brilliant, a unique take on modern Greek food. I haven't been there for lunch but I believe the experience is similar to the evening one. Voted "Best New Restaurant" and "Chef of the Year" in
The Age Good Food Guide 2008.
- Snaggle.