Local buses run along the coast to remote hotels and sanatoriums.
Ochakiv is a typical summer resort place where tourists (mostly from Ukraine and Russia) go on vacation. There is a lot of sun, fresh vegetables and fresh water of the Dnieper pouring into salty water of the Black Sea.
The old Russian border fence along the coast is cool to see, no passport needed to cross onto the beach anymore.
Ochakiv Military History Museum of O.V. Suvorov
Olbia, an archaeological reservation, near the village of Parutino.
Cross the Dnieper estuary by daily boat from the port of Ochakiv to Kinburn peninsula to see National Park "White Bank of Svyatoslav" and the "Volzhyn forest".
Beach, Beach, Beach - they are plentiful and wonderful.
Restaurants are hard to find, as the inner city is pretty much dead. Grocery stores are around though. Bring your own food or be prepared to eat at an "OK" beach bar-type place.
Ukrainian beer is very cheap at the beach-bars. There is not much nightlife (one club?) so hang out at the beach at night or go to bed so you can spend the next day at the beach.
Renting a house is pretty much the only way to go. Look for people with signs at the auto station ("autovakzal"). Rent is very inexpensive for American visitors... provided that you speak Russian. Prices will surely go up if they think you are a foreigner.
Hotel "Fort Gelios" price list (in UAH) 
Catch a cab or a van to the auto station ("Autovakzal"). You can catch a ride to anywhere in the region for a few dollars.