As far as independent restaurants, any of the above options, plus:
Sage Garden Cafe in the Wilson's Nursery Center:
http://wilsonnurseriesky.com/sage-garden-cafe/Super popular since it opened last year, but you can expect a wait for a table if you arrive between 11:30 am and 1:30 pm.
The Meeting House B&B (downtown) has a cafe open for lunch on weekdays:
http://www.themeetinghousebandb.com/cafe.htmlJim's Seafood on the KY River is popular with the locals (if you're in the mood for seafood):
http://www.jimseafood.com/Serafini's (downtown) is a more formal setting where legislators tend to congregate this time of year.
http://www.facebook.com/pages/Serafini-Restaurant-Frankfort-KY/148791965144965