Once in Batumi, take a lazy walk at Batumi bay area, watch ships on anchor and enjoy a cup of tasty Turkish coffee at some of the bay cafeterias.
From Batumi bay you could take an aerial tram and get some really spectacular views towards Batumi.
Boulevard at Batumi bay
Ship on anchor at Batumi
You can climb down from the boulevard and enjoy pebbled shore.
Cargo ships at Batumi port
And really spectacular views towards Adjarian mountains,