Our family of 4 just got back from our stay in Ischia and we thoroughly enjoyed it! The kids loved the swimming pool and the apartment was very close to everything in Lacco Ameno. I think my wife and I loved the porch the best as it provided a private, great view of the town and water.
The kitchen had everything we needed, though we didn't really cook that much. We just made coffee, cooked eggs in the morning, boiled water and warmed up leftover pizza in the oven.
As for the apartment, I would call it a traditional Italian residence. We loved it! Be warned that means no air conditioning. We didn't mind as the weather was beautiful and the ceiling fans in each room made for comfortable sleeping. The apartment does overlook the main road so you need to lower the blinds for noise to block out traffic sounds and to darken the rooms.
The apartment's location is great, right at the beginning of Lacco Ameno. You can walk to everything including restaurants, beach, grocery store, etc. We did rent scooters to explore the island but they aren't necessary for Lacco Ameno access.
A couple of notes related to the swimming pool: First, the hours of operation. Everything in Ischia shuts down beginning at 2 pm until 4 or 5 pm, including the pool. We used that time to eat a late lunch and read before heading back to the pool. Second, just a warning that you have to wear a swim cap (provided in the apartment) to use the pool. Our boys didn't really want to do that at first, but they quickly got used to it and it was not a big deal. I only mention it because it was kind of a surprise.
We would definitely stay there again!