Would need to know more about your situation. What country/city you are in and what your general business model it. Unless you sell alcohol and are aiming for adult AL games, I think it might be hard to see AL helping your bottom line unless run at a slow time that you remain open anyway.
Game stores have incentives for bringing organized play in as they increase opportunities for players to buy merchandise while at the store. Gaming stores can add to this by selling food, drink, and charging a small table fee.
For a restaurant, coffee shop, or bar, is a table of gamers buying enough food and drink to cover what you need to make for them to take those spots for 4-6 hours? You could charge for the use of the space or set a minimum order fee, but you may find it difficult for people to pay that, especially on a weekly basis.
I don't want to discourage you. I really hope you find a way to make this profitable because it would only help the hobby. But, in America at least, I think it is a challenge to make money off of providing gaming space.
This is one thing I miss about living in Taiwan. Because space is at such a premium, people are willing to pay hourly fees for space at clubs, bars, cafes, etc. Back in the 90s in Taipei and other large cities, they had these great lounges where you could rent a large comfortable chair and table to a large table with sofas and chairs, to a private room. They had a large library of comics. You paid an hourly rate that would include tea, snacks, and rental of comics, and you had a button at the table to call wait staff to order meals, alcohol, etc. I wished I had a gaming group when I lived their, it would have been a great place to game.
In America, even in cities like New York, it is hard to find venues like that. Actually, on my last trip to New York, I joined a game group that met in the basement of one those cafe/buffet/convenience stores that you see all over the place. In the evening the lower level was empty evening the the store was open for people walking in to get snacks, cigarettes, bachelor dinners takeouts, etc. So we didn't pay a thing to take up a couple large tables for a few hours. They didn't mind because we were buying drinks and snacks and they were not otherwise using the space.
Where I have seen it work are at game stores. My kids and I go to Fantasy Flight Game's gaming room and cafe a couple times a month. We bring our own games or play games from their library. We pay about USD 25-35 for food and drinks for the three of us (when I game there with my friends, it is much more, because beer) and we take up a large table for about 3 hours. But Fantasy Flight is a game publisher. This space and cafe are not how they make their money. It helps support their products by giving people a chance to play their games and by hosting events there. Also, I rarely leave there without paying 15-30 dollars on SOMETHING from their store. It is not uncommon for me to plunk down a $100 or more on board games.
If I owned a cafe or restaurant here in Minnesota, I might try the following.
First, I would want to have space set apart from other customers, if not an event room, then tables off to the side.
Second, gamers like big tables. If you only have small square or circle tables, I don't think gaming events will be very popular.
Third, I would avoid hosting campaigns. Instead, start with everything-included one-offs. Partner with an experienced DM and come up with some profit-sharing arrangement. Run a 4-hour event with a cover charge that includes a meal, maybe unlimited soft drinks, all gaming materials, and I would try to work with a DM that can provide terrain and minis, etc. Maybe have the table set up near a flat-screen display for use of digital aids.
Maybe, in your area, if you provide a great experience, you could charge 20-30 a seat for Dinner and D&D. Problem is for many players that price might seem high, even though you easily pay that for 45-60 minutes having dinner at a lower-end restaurant. Also, if you have the seats taken up for 4 hours, $5-6 an hour per seat isn't that great, especially if you are paying the DM in money or free food. I think it might make more sense if you (1) own the cafe and (2) are the DM. So long as you are not losing seats to more profitable customers, it might be a good way to enjoy combining gaming with your cafe business.
Best of luck with whatever you decide. Please post back with what you decide to do and let us know how it goes.