I know that I'm not familiar with many of the weekly specials that several places have and I've posted a thread before with some but thought I would once again start a topic and hope that others might contribute their knowledge or experience regarding some special offerings.
Every Monday night/evening Sam's Grille in Florence, the old Demo's building, has buy one entrée get one free as long as you purchase two drinks.
Every Wednesday Pizza Hut has their Wing Night specials
Every day the first customer's at Buffalo Wild Wings get a free appetizer
Waffle House offers a 10% senior discount if you qualify and ask for it.
At Buffalo Wild Wings Tuesday has traditional wings on sale and Thursday the boneless wings are on sale
Mon-Wed at Logans they have a two for $15.99 selection menu
Tuesday Nights is Family night at Blue Coast Burrito with special prices on some items
Thursday's is Kid's night at Captain D's where kid's meals are $0.99 ea
Kid's eat free (or used to) at Lenny's subs on Sundays.
Ricatonis Italian Grille has All you can eat Spaghetti & Meatballs on Sunday Night and Monday's and it comes with a salad. Last I checked this special was still in effect but they were contemplating some changes.