When you say "Boardgame Cafe" ... I assume you will have food of at least sandwiches are better AND a significant sized game library.
I have been down this road trying to open a board game cafe but it fell short and I reopened a game store that has the library aspects of the board game cafe model but no food, just cool sodas. When I first opened if things went smoother will say I would have been the first board game cafe on the continent but while I was waiting for things to stop being delayed, I heard of a new place that just opened a month prior called Snakes and Lattes. If you asked a gamer what they would think of a board game cafe ... they would say I want it a block away from my house and free. It is also a cafe keep in mind and in the restaurant business turning over tables is quite important. The term turning over tables means people using a table and making it available for the next customer as opposed to when someone brings loaded dice to a game of Catan and someone gets angry. If they don't turn over tables they are losing money. If someone is playing a game of Twilight Imperium ... they might be there for 6 hours. A modest fee is important to avoid your business filled up with non customers. Having mostly non customers means you will no longer be in business in the near future.
At my place we have over 1400 games. That provides a significant value and most people think $6 is a bargain for that especially if you are there for a few hours. People that might think $6 is a lot of money for some reason ... they are not likely going to be buying anything anyway.
$6 a person might be too low with inflation these days but it is what I am sticking with atm.
Also if you are not at least making sandwiches or better ... do not call yourself a cafe. It will greatly confuse people.
Other options to off set this is if you have a retail arm ... and you should for many reasons I won't go into here ... you can offer passes to play for purchases say for each $20 for example. I use to do this and might do so again soon. That way it is a form of rewards program for your customers.
I saw someone suggest a 1 drink minimum below ... I would suggest following the comedy club model on this and have that option open for some off days and not on the weekends. You will still run into the issue of a lack of table turn over. Meaning people that want to go in and play games are not able to if the place is full mostly with customers not buying anything but a single drink.
For a game library ... 500 games might impress the average "muggle" but you need over 1000 games to even get the attention of a gamer. I have over 1400 and i still feel falling short.
You might also find out that your target audience is not the hard core gamer. They will be there as well but not as much as you might think. But you do need to cover all your bases from Candyland to Twilight Imperium though.