Due to the presence of Japanese and Korean industry, Chennai has one of the largest diasporas from those countries in India. Some restaurants to check out over your month in Chennai (which will also show you the different parts of the city):

• Kuuraku (also in Mumbai and Bangalore, they do Yakitori)
• Hokkaido Japanese Restaurant (they do seafood)
• Oyama (really solid Japanese style curries)
• Dahlia (very very low key ramen spot)
• Aeseo (solid Korean food all around and also has a karaoke floor)
• Another Kitchen (proper KBBQ)
• Tokyo Diner (hidden inside a bakery, they do a 10 course omakase Japanese fusion menu, you’ll have to find it on Instagram, not on Google maps)

Not quite Japanese or Korean but Avartana at the ITC Grand Chola gets a lot of praise for its South Indian seafood focussed tasting menus. Also the Farm is a bit away from the city proper but is a very very solid farm to table restaurant (established around 50 years ago) and farm shop (if you wish to buy fresh veggies while self catering).