If you're looking for a sit-down dinner at a Louisville restaurant today, Open Table indicates that Morton's Steakhouse, Mitchell's Fishmarket and Buca di Beppo all have seating available. Ruth's Chris, the English Grill and Rivue are open but booked up.
http://www.opentable.com/promo.aspx?m=43&pid=6
I'm informed that Bombay Grill and Dakshin are both open; other Indian restaurants may be. Some Asian restaurants, including Chinese, Korean, Vietnamese and Thai may open ... it's best to call your favorites to confirm.
If you know of or discover any other popular spots open, feel free to post here.