I would suggest creating videos for social media that show off the business. The cat cafe can reach out to other local businesses and partner up to give special discounts or experiences; for example a local bakery or music store. Fliers and business cards are always a good way to get their name out in the local community, maybe with 5-10% discount on purchase code or something. You could also advertise on your social media and recommend them to your friends and family.
There are plenty of opportunities to give the cat cafe exposure and there are no bad ideas!
I would suggest involving the biggest differentiator of your local café which should be the cats.
Here is an example of a smart and successful promotion campaign having llamas in the middle of a campus. https://universe.byu.edu/2014/04/08/llamas-invade-campus-to-promote-humanitarian-organization/
So, if you can get the cats somewhere nearby the café and show people what nice animals they are, you would create some buzz.
Why not trying to arrange some local events, like networking, game nights, movie nights?
Be on social media as much as possible, everyone has the phone in their hands most of the day. Post on social media, arrange events, post daily pictures.
I hope this helps.
Doina recommends the following next steps:
Hi Avonleigh, it's great that you want to help a worthy cause. Your friends and family can be great tools when you're trying to bring attention to a person, place or thing. Ask for their support by stopping in and/or spreading the word to their own friends and family. Word of mouth is a powerful tool. Check in on social media and ask others to do the same. Create a "buzz" that will make other people curious and want to come see what everyone is talking about.
Kimberly recommends the following next steps: