First step: create a FB page (not FB profile) then put your business link into it.
Next step: create ads on FB. You can customize detailed profiles that you want from FB users, such as gender, city, language, relationship status, age and more. Directing an ad toward the FB page.
You can select your town through the ad on FB. So you can attract people who live at your town toward your FB page.
At the ad page, you can input "interest" into the field and you can get more targeted people from the FB.
Twitter - you can insert your Twitter url into the FB page. This can directing people who from FB toward Twitter then you get new followers at your Twitter. If you make a tweet on your Twitter then you post your tweet link into the FB page.
Thus you can use both FB and Twitter for your local business by targeting local community of your city/ town.