We've stayed in Nissaki many times (ten I think!) always in late May/early June. Small children (and their parents) always seem to have a great time on the pretty little beach. The water is shallow and warms up quickly so even that early in the season it's very pleasant. Kids seem to enjoy collecting pebbles and don't seem to miss having sand. You can hire sunbeds and umbrellas, and when you want a drink or a snack it's just a couple of steps up to Mitsos taverna from where you can watch your kids playing with all the other children they will have made friends with.
With a car, you can explore the other small villages and beaches up the coast but in my opinion Nissaki is the prettiest. Do be sure also to visit Corfu town which is one of the loveliest towns in Greece.
We have been going to Nissaki with our little girl since she was six months old. She is three this year and it will be her fourth visit. Agree with all of the above and find it to be a safe and friendly resort. The small beach sometimes gets a bit crowded at lunchtime with day trippers, but when they leave it is peaceful again. All the local children play together with the tourists and become great pals. The local tavernas are all excellant and welcome youngsters with open arms and plenty of treats. All have high chairs. If you head north on the coast road there are some beautiful beaches with great tavernas. if you feel capable you can hire a boat for the day and visit many coves up the coast. A great day out for about 60 euros plus fuel. Very safe with tuition (if required) and all life jackets included. Have a great holiday.