It should depend on what you are keen on.
1/ For cultural and historic sights:
Cham museum: This is a museum of Chăm ancient statues. This is the best place in town to know about an old style of architect in Vietnam. There would also be notes for you to know about costumes, belief, etc. of Cham people. Ticket for an adult is about 40,000 VND (less than 2 USD).
Linh Ung pagoda: lies on Monkey mountain (Son Tra peninsula). This is a Buddhist temple, with an enormous statue of Lady Buddha. It has wonderful skyline and city view (local guaranteed), and the gods are very blessing to who is sincere.

Marble mountain: 5 mounts represent 5 elements (Fire, water, metal, earth, wood), but actually only visiting Water mount is enough. There are a lot of caves and temples to discover, and you can take the long stair or an elevator up to the top.
These are a few historic sights. There are various tours to join, it’s up to you if you want to be instructed, or discover it yourself.
2/ Feel it like a local:
Local market: Han market is especially designed for tourists (the ladies can speak English and some Chinese, Korean), not too crowded in the afternoon and clean enough. 2 floors to discover. Con market is mostly for ones who can stand a local super crowded place, and should be very careful with your pockets. But the food here is soooo yummy.
Coffee shop: Try Long coffee (a must know shop in Danang), sit down on a kindergarten chair and try black coffee/coffee with condensed milk. Enjoy the vibe. Don’t drink all in a shot.
Food to try: Banh xeo (crispy pancake), banh beo (water fern cake) and my quang (Quang noodles). Danang also has super good seafood, with various price (I like Ba Thoi one, fresh seafood and not too costly).
August is the last season in the year to go swimming in the sea. September may have bad storms. But I guarantee that the seashore is wonderful. Soft golden sand and super clean water (the city is really strict about littering here).
If you are into cooking, try a cooking class indeed. Cook, think and eat like a local. You will even be introduced some good places to try local dishes (which are not in class menu).
Asian Park: a newly built amusement park. Quite beautiful and interesting, especially during special festivals. Entrance ticket about 300,000 VND/adult. Many tourists come here, but I wouldn’t highly recommend for those who already visited Disneyland.
3/ Around Danang
My Son sanctuary: an old temple of Cham people, built around 4th - 14th century. “A cluster of abandoned and partially ruined Hindu temples”, they worship Shiva, with symbols like Linga & Yoni. It lies about 68km from city center, ticket for adult is 100,000 VND/foreign tourist.

Hoi an: A MUST VISIT ANCIENT TOWN. It is only 30 km away from city center. Local loves it. Tourists love it. Day and night. And if you miss the beach in Danang, you can also try An Bang beach in Hoian.

Ba Na hills: 25km from city center. Beautifully constructed French village, it looks like beauty sleeping in the fog. Quite touristic during weekend. Entrance fee about 650,000 VND/adult, including cable car, ticket to all temples, and most of the games. There is an interesting wine cellar on the way to flower garden (may cost you about 100,000 more to go there).

It seems like a long list of places so I attached some photos for reference. To be honest, I would recommend these: Han market, local coffee, beach, Hoi An and Linh Ung pagoda for a checklist.
Hope you will enjoy your trip in Da Nang. Cheers!
Ps: These are personal opinions from a local. If you are a real risk taker who wants to ride motorbike around the cities, there may be more to go.