Kuching has a bit of a reputation as a popular foodie destination. It's nothing like Penang, but there are a number of good restaurants around town. The Waterfront park is full of food kiosks that are only open at night, but the consensus is that most of them are pretty awful. Try them at your own risk. If you want to dine by the riverside, then the best option is the James Brooke Bistro near the Chinese Museum.
Away from the waterfront, one of the best areas to find lots of dining options is Padungan Road, a short walk away from the waterfront. The street is lined with restaurants of all cuisines, as well as several friendly pubs. Restaurants in tourist areas come and go, so you can check my travel journal for the latest reviews of Kuching restaurants.
Local dishes you'll want to be on the look out for include the Sarawak version of laksa, a spicy noodle soup that is popular throughout Malaysia and Singapore. However, locals consider their version of laksa to be far superior to others, and it's hard to argue with them. Another local dish is kolok mee (sometimes kolo mee), thin egg noodles served with sliced roast meat (traditionally pork, although halal versions use beef) and spices.
There are several coffee shops around Kuching, including both internationals chains as well as some of the local favorites. You can of course find all of Malaysia's local food chains in the malls around town.
It's worth noting that many restaurants close at least one day a week, usually either on Sunday or Monday.