The site we used to use regularly was Restaurant.com. Restaurants will use them to advertise themselves in order to increase their customer base and customers can get gift certificates that they can use for half their face value (i.e. pay $25, spend $50; pay $12.50, spend $25). They often have sales where you pay less than half of the certificate's face value. It's a great way to try a new place out. I would advise, however, that you contact the restaurant before you buy the certificate just in case they've stopped accepting them and haven't yet told Restaurant.com. Always ask upon arrival, too, just in case. It's not often that it happens, but it does happen and you should not wait for a surprise before you find out. Restaurant.com will credit you with the money for the purchase, though, that you can use on another purchase of a different certificate, so you really don't lose your money.
Each restaurant has its own rules that apply to the use of the certificates, so be sure to read the fine print. Some require groups of four, some restrict to certain days of the week, etc. Be sure you know what you're paying for before you buy. Once you've bought the certificate, print it and tuck it away to take with you to dinner.
We have also used these when we're traveling if we've planned our stops in advance. It has saved us more than once during a road trip.
Another way is in the weekly or monthly coupon books that arrive in the mail. They will often have BOGO or other deep discount coupons for local restaurants in them that expire at the end of that month or the next.
The Entertainment Book is another source of discounts if you're willing to pay the price of the book itself. End of year discounts on the book are a good way to go if you realize that their year ends November 1. My daughter and I have used these for years. She makes full use of the movie coupons and my friend and I use the restaurant coupons, but it doesn't take long to recoup the original cost of the book. And, restaurants aren't the only discounts being offered. There are other discounts that the Entertainment Book has such as car washes, auto maintenance, lawn care, car rental, etc.
One of the restaurants we visit that has a "Sunset Menu"
Locally, several of our restaurants have what they refer to as "sunset menus", a type of "prix fixe" menu, that are only good between the hours of 4PM and 7PM (generally). They offer a more limited selection, but also often include beverage, soup, salad, entree and dessert, for a lower price than their main menu offers just for the entree. We have really enjoyed using that option.
All in all, there are quite a few ways to enjoy dining out at a reduced price even when your budget is tight. Even if it's only once a month, we all deserve to treat ourselves once in a while.