When we stopped at Tanjung Aru we used to take the hotel speedboat and spend some of the day on the beach at nearby island of Palau Manakan which had a nice beach and good snorkelling. For eating out we used to catch a taxi into Kota Kinabalu (5 mins to city centre) and eat at the various restaurants. This was a while back so I can't give any specific recommendations for eateries but the principle remains the same.