We stayed for 10 days with our son aged 4 and had a great holiday.
Nice as a city is great for kids - there is a massive play park in the city centre which our son loved and caters to different ages. On top of the mountain (which you can reach by lift) there is a great view and more play areas. Obviously you have the boulevard and beaches as well.
We rented a car ( good private parking in the basement) and drove 35min to Juan les Pins a couple of times to enjoy the nice sandy beaches too.
The weather was so so for the first few days, but when it turned better it was perfect and we were able to enjoy both the Big pool and small pool. They are not heated, but in particular the small pool is warm enough (half May) when the sun is out. In summer both should be perfect.
The apartment is very well appointed, modern and clean.
It worked well for the 3 of us, but unless the 4th person is very little (eg baby) it is probably a tad small for 4, unless you spend all your time on the beach and only use the apartment to crash for the night.
Our son was in the bedroom whilst we slept on the sofa-bed in the living room, so that we were able to enjoy a glass of wine in the evening on the balcony which has an absolutely fantastic view (stunning both day and night)!
The sofa-bed slept very well for duration of the holiday (despite us being 6'4) and is very easy to set up and tidy away again.
Noelle who organised the bedding and towels on site - was very welcoming and friendly. As noted in some other reviews she only speaks French, but that was fine for us.
Location wise, it is only a short stroll to the harbour down the hill. On the way back, we pushed our buggy up which is fine as long as you are reasonably fit. When we were tired from a days walking we also took the 30 or 80 bus up a couple of times, which are frequent enough, easy and cheap.
There is a big Supermarket about half a mile away. We walked it twice, but with heavy bags car is better.
If we had to provide any negative comment it would be that when you walk into the apartment you walk straight into the bedroom (as it is a former hotel). Practically speaking this wasn't an issue though and after a day or so we had got used to it and barely noticed it.
All in all we had a fabulous holiday and hope to come back!