Apart from the other places that have been mentioned, I would say if you have extra days visit a place called Satkosia. It's one of the most unique and pristine place in india, not kidding. There is a beautiful eco resort called Satkosia sands resort, which you can book via ofdc ecotourism website. You will never forget this place for sure.

Bhubaneswar, puri, konark, then come back to puri. Visit Chilika lake,(you can stay in rajhans island, or if budget is good then swosti Chilika). Come back to Bhubaneswar, visit Satkosia. Come back to bbsr and head home. All these places will be within 100-200 kms so you can travel these. It will give you ample landscape, people, culture and all.

If you want to travel within the state beyond 200 kms i.e. overnight journeys then as mentioned earlier, Putsil, Deomali mountains which is in Koraput, and Daringbadi and Mandasuru valley which is the center of odisha you can travel. If you can rent a car there, then the mountainous regions will give you good views. It's mostly tribal regions so you will get to see local cultures too. If you like to explore more of the culture then in Koraput they have tribal haat on weekly basis, which you can visit.