Cala Llonga is just 5 minutes drive from Santa Eulalia and has one of the best beaches on the island. It is one of few to consistently get blue flag status. It's a very family friendly resort and my kids (and a long time before that, my sibling and I) love it. The sea is pretty shallow till quite far out and has a nice play area so it's perfect for younger children, and they will see fish swimming with them! We spend a lot of our evenings in Santa Eulalia where restaurant choice is wider. It has a very relaxed vibe, a mix of restaurants and a beautiful sea front to stroll along of an evening. For a special meal check Chiringuito Blue but CBBC Marina is also nice and surprisingly child friendly.
Car hire this season is expensive and whilst we have our own car, friends that visit regularly are just using taxis this year. There are ferries operating along the coast and are also a nice alternative to get around, it also means we can have a glass of wine.
Personally I would stay in Cala Llonga as the beach is so much nicer, however the main hotel is being refurbished this year so options are limited (there is another hotel on the other side of the bay), there are also lots of self catering options. I would then suggest ferry or taxi to Ibiza town one night or Santa Eulalia. However staying in Santa Eulalia is also a great option if you get a nice hotel with pool and don't mind a more crowded beach (it's man made).
Ibiza town of an evening is also nice, there is a great ice cream parlour just as you go up the ramps into the old town, kids love it. We have been known to take our own bottle of wine to the top and watch the world go by while the kids run around.
Es cana is also family friendly and walking distance to Cala Nova, but these beaches have got increasingly trendy in the last few years and my heart weeps a little at the loss of the more boho beach shacks, replaced by the Instagram hounds. Check out Atzaro beach on Google for some images, we go off season but don't attempt it in the summer when the thong crowd hit it.
Hope that helps!