Take a day trip to Kinabalu National Park and do the canopy walk? Visit the Australian Death March Memorial which is nearby.
Or to really get out, go to visit The Tip of Borneo but this will really take a FULL day!
Restaurants? Geez! I don't know the names, I just go there (local boy)!! For seafood, Ocean Village next to Promenade Hotel, Grand Port View at Waterfront or Alu Alu Restaurant near Jesselton Point. (tends to be a bit expensive nowadays as they were spoilt by the Chinese tourists)
The Ox tail dish at Hyatt Hotel is not to be missed! Bak Kuh Teh across Jesselton Hotel, 5 Star Chicken Rice at City Mall.
PM me if you need further info.