One place to start is with the Greater Madison Convention & Visitors Bureau which has a page on Restaurants. You’ll find that the Downtown Madison Map & Guide has the restaurants located on a physical map (oddly it isn’t online so you need to pick up a hard copy).
Famously, Prof. Miles Hanley, Associate Director of the Linguistic Atlas of New England, died in the old Fess Hotel (in the picture above) which is now a brew pub (a good place to raise a toast to fieldwork, car batteries fueling 1930s recording equipment, and seat belts, &c.).
NWAV46 is a harassment free conference (See NWAV policy and UW System and UW-Madison policies)