We've been to La Palma three times and every time we've decided to stay in the same complex. Why? Large apartments, good price, and there's still a feeling of luxury provided by the Hacienda San Jorge (restaurant, shop, large pool, gym, gorgeous botanical gardens, bar, music.) The complex is very peaceful, there's a lot of privacy, amazing view from the large balcony's and it's safe for small children. Stayed in three different apartments, the last one we stayed in was the nicest. The interior isn't really that important to us, as long as all the appliances work, the beds are comfortable and the food is ok. You need to hire a car. If you come off-season you should shop around: don't be afraid to haggle over the price (doesn't work at the height of the season.)
All in all: Simple, cheap apartments with an option to use the luxuries of the complex located nearby. All this on a beautiful island.