As in most destinations, location is an important consideration when selecting your hotel. Most of the main sights of Kuching are within easy walking distance of each other, so the best place to stay is near them. The Hilton is right on the waterfront and an old favorite, but the new Pullman, opened in 2010, on the hill behind the Hilton probably has the best views. If something smaller and more distinctive is what you're looking for, then the Batik Boutique Hotel is an award winning small hotel in a good location. The best budget option is probably the LimeTree Hotel. It's about a 10 minute walk from the waterfront area, but is very close to a lot of nice restaurants and pubs around Padungan Street.
Below is my list of all the recommended hotels. If you don't like my choices, you can use the search box at the bottom of the page to find the best rates by searching dozens of sites at once.