All major sights around the Dnister estuary can be easily visited in one long day using suburban trains and marshrutka minibuses.
Although there is a huge amount of (mostly mediocre) accommodation in Zatoka and Karolino-Buhaz, you don't really need to overnight in the area, because all the sights can be done in one day.
There are a few summer-only cafes inside the Akkerman fortress. Zatoka and Karolino-Buhaz are dotted with cheap eateries of varying quality, pretty much all of which close in winter. There are a few better choices in the centre of Chornomorsk. The only really decent restaurant in the area is located in Shabo.