I Visited Kota Kinabalu in April 2015. That Trip is the cheapest yet the most treasured trip i ever had. Center Point is where i get off on my way to the city center from KK International Airport, Its only 10 Minutes ride from the Airport, Fare is 5RM by Airport Bus and 30RM for Taxi. Just to give an idea about Center Point, it is a busy Mall located in the center of Kota Kinabalu. Inside the mall are small stores selling cellphones, Accessories, Gadgets, Fashions etc. Food Court on the Lower Level, Entertainment and Theater on the Fifth Floor. Nearby are Hotels, Lodges and Backpackers easier for Tourist to just walk around and choose a place to stay.
By the way, for info before riding a Taxi in Kota Kinabalu be sure to negotiate your fare to the taxi driver first before riding because taxi in KK don't use Taxi Meter.
In my solo adventure walking around the city i came to see KK tourist spots like City Park, the only park in the city center just opposite the court complex. It contains the British North Borneo Memorial which commemorates the soldiers who fought and died defending the British Empire in WW1 Built in 1923.
I also visited Atkinson Clock Tower one of the land mark of KK, Located on a Hill beside Jalan Tunku Abdul Rahman a few minutes from the city center.
Interesting part is to View the Beauty of the City Center, just walk up to Signal Hill Observatory around 10 Minutes from Atkinson Clock Tower.
In the evening i usually go to Philippine Market., located near oceanus water front, there i can buy cheap sea foods, fruits and vegetables, food center also available inside the market at affordable price. For best shopping deals and place to unwind walk around Gaya Street after the Arc Gate. There you can find lots of Local Food Centers, Restaurants, Coffee shops and Shopping Stalls. You can also visit there Sunday Market in the Morning.