Lots depends on your budget, but I would avoid staying in St Helier - other parts of the island are much more scenic. I’d suggest staying in St Brelade’s Bay (beautiful beach with lots of space for a small person to run around). There are a number of hotels down there (happy to advise on options if you PM me). The Oyster Box restaurant in the bay is good too.
There’s also the Atlantic Hotel overlooking St Ouen’s Bay which is lovely (sophisticated but family friendly with beautiful grounds overlooking the sea) and an excellent restaurant.
The island has great restaurants and cafes - it depends on what you are looking for. Taxis are plentiful, and the places I’ve suggested are ten minutes’ drive from the airport. Message me if you need more advice.