2 weeks in Okayama is a blessing. I could make quick use of that time for sure! Definitely not too long!
Okayama has a lot of tasty food specialties. Demi-katsudon, Okayama bara-zushi, Kabakuro Maeda, an entire fruit parfait guide (Contents Cafe during the peone parfait season is my favorite), mamakari, etc. The only thing about Okayama's specialties are that so many are seasonal.
As far as nightlife goes, Okayama has a decent number of bars. Although I know Okayama's sites very well, sadly nightlife is something I don't do enough, so I don't have advice on what specific locations are the most fun...
Within Okayama City, there are a lot of interesting places aside from Korakuen Garden and Okayama Castle.
First, have you visited the other attractions within the "Culture Zone"? I like Yumeji Takehisa's works, so the Yumeji Art Museum is great.
The Hayashibara Museum has lots of Important Cultural Properties and National Treasures. The Orient Museum is a nice look at Middle Eastern art and artifacts. The Prefectural Museum of Art may be worth it depending on what the exhibit will be during your stay even if you've been there before. The Prefectural Museum is also nice.
The Okayama City Museum (formally Okayama Digital Museum) has hosted some excellent exhibits. Check what they will be featuring during your stay.
Outside of that, the Kibi Plains mentioned above are well worth it. Off the main trail, the Ashimori area is quite nice. There is a small historic district and Omizuen Garden is beautiful and free to enter.
Saijo Inari is one of the top 3 inari shrines and it's nice and impressive.
Sogenji Temple is quite surreal. The temple itself is nice and has a small garden, but what really makes it stand out is that most of the monks/priests there are foreign Buddhists. It may not be the most PC thing to say, but it really gives an odd feeling, sort of like a Star Wars scene.
You can book a tour of Kirin Beer Park.
Inujima Island is a world-class art island that is highly recommended!
For other Okayama City ideas, these are good:
https://en.wikivoyage.org/wiki/Okayamahttp://members.virtualtourist.com/m/a40e1/ed3c9/http://www.japan-guide.com/e/e5725.htmlThe above are all within Okayama City limits.
Going beyond, there are a million more options:
-Bizen (Shizutani School is the world's first integrated school; it's attractive and interesting. The Bizen Pottery sites are interesting and making your own pottery is fun. The Hattoji area is home to Hattoji Villa if you want to stay in an old Japanese farmhouse.)
http://www.virtualtourist.com/travel/Asia/Japan/Okayama_ken/Bizen-2272...http://www.international-villa.or.jp/villa/hatto0904.htm-Kurashiki (The most famous place in Okayama with its large historic district and museums)
http://www.japan-guide.com/e/e5750.htmlhttp://members.virtualtourist.com/m/a40e1/edca1/-Takahashi (Home to Bitchu Matsuyama Castle, the only original mountain castle in the nation and also the highest. The town below is interesting. The Fukiya area is a beautiful historic district that also has interesting sites, such as the former copper mines and old residences)
http://www.japan-guide.com/e/e5775.htmlhttps://en.wikivoyage.org/wiki/Takahashi-Tsuyama (A charming former castle town with impressive castle ruins, the beautiful Shurakuen Garden, Horumon Udon, and a nice historic district):
http://members.virtualtourist.com/m/a40e1/ec873/-Maniwa (Home to the famous Yubara Onsen, a "yokozuna" of rotemburo - outdoor, open-air onsen, award-winning Hiruzen Yakisoba (worthy of the awards, too!), Kanba Falls, and the Katsuyama "noren town")
http://okayama-japan.jp/maniwa/en/http://members.virtualtourist.com/m/a40e1/22ab76/-Niimi (Home to 2 caves and a waterfall, popular among nature-lovers)
-Yakage has a nice, quiet historic area.
-Soja has Kinojo Castle, one of the first castles ever built in Japan and Iyama Hofukuji Temple, along with a small part of the Kibi Plains, shared with Okayama.
Okayama is also a great base for exploring Kagawa Prefecture (and other places in Shikoku), Western Hyogo, Eastern Hiroshima, Izumo, Matsue, and Tottori.