We have stayed at a lot of hotels in South East Asia in our travels. Some good, some bad, and some beyond belief. Here are some we have stayed in, and feel we can recommend.
Keep in mind, with Kuta it is a good idea to work out which area you wish to be in - central Kuta Beach, around Poppies lanes, is good for cheaper, smaller hotels, and close to the surf action, whereas Seminyak, to the north, has many of the newer, luxury resorts, as well as the most sophisticated dining scene. Legion, between Kuta and Seminyak, as well as Tuban, to the Airport end of Kuta, both have many family type hotels, with kids clubs, multiple pools, and large grounds, where the kids will need less supervision. In all areas, the larger hotels will generally be the ones with direct beach access, with many of the cheaper and smaller hotels on Gangs (laneways), and on streets one or two back from the beach