The bar so fun that makes you need to apologize to your grandmother (Bebo, in Georgian, is how you might address your grandmother) is located in downtown Batumi.
They offer hookah, cocktails, and Georgian craft beer (Shavi Lomi). They have great bar food, too! Mainly burgers, fries, pasta, and fried chicken, all delightfully greasy.
Although they close rather early for Batumi, at midnight, it is a fun, relaxed place for a first stop on a night out, or even lunch after a day at the beach!