Monday and Tuesday? Really?
IMHO the best steak is at The Peerless restaurant in west Knox, off Cedar Bluff Road, on North Peters Road (there's also a CycleGear close by if you need a motorcycle shop fix.)
Great, traditional Italian: Naples. In the "Bearden" district, on Kingston Pike. Follow this up with a visit to The Casual Pint off Northshore Drive (very near Naples)
Otherwise spend your time in/around downtown. Market Square and Gay Street are it. Preservation Pub. Peter Kern Library (a terribly cool speakeasy in The Oliver Hotel), Downtown Grill & Brewery, if you're into opera The Barber of Seville is at The Bijou. Tomato Head Pizza... It's a great area. Enjoy!