Lanzarote is a small island and it takes around one hour to drive from one side to the other. Anyways, depending on the type of holidays you are looking for or the tourism you are planning to do, some areas are better than others. To recommend areas I am guessing already that you are renting a car because otherwise it is very difficult to get to most places.
Before anything you should know that the weather changes between the north and the south. The north is more windy and it has a few degrees less than the south. It can be the case that the north is cloudy, windy and even raining and there is sun in the south.
If you are looking for a touristic area:
Playa Blanca has always been a touristic area but nowadays even more. There are hotels, apartments for rent and most of them have swimming pool.
The best thing of this area is that there is normally good weather even though in the rest of the island there isn’t. Furthermore, because this is a touristic area there are a lot of different activities to do, like going for a walk in Marina Rubicón (a port with restaurants and a mall), practice scuba diving or snorkeling.
If you are traveling with children this is also a perfect place because there is water park and small beaches to be able to watch your children at all time. The famous beach Papagayo is also very nearby and there is a port where you can take a quick bout to Fuerteventura or Isla de Lobos.
The bad thing of this area is that it is very focused on tourism so the prices are higher and it’s more difficult to find local food. Apart from that, if you are going to do tourism for a few days you will feel like you are far away from everywhere else.
Puerto del Carmen (Fariones)
It is also a touristic place but older compared to Playa Blanca. Not every hotel or apartment has a swimming pool and this area is not so well cared for like Playa Blanca. Despite that, if you are looking for a place with people and easy access to the beach, Puerto del Carmen could be your place. Furthermore, it is well located if you are moving around by car.
This area has the same problem with restaurants like Playa Blanca, it is difficult to find local food, or even Spanish food.
Costa Teguise is a touristy also but lesser known. It has a nice avenue walks and different beaches. You can also attend windsurfing classes or go to the waterpark if you are traveling with children. The location is good but it has the same problem with restaurants as the previews places.
Puerto del Carmen (Fariones)
If you are looking for a quiet place:
Matagorda is located near Puerto del Carmen and they are connected by a bicycle lane. There are also hotels and apartments for rent in this area but it’s not as crowded and its well cared for. It is true that the beach here is not the most beautiful one but it’s a quiet area and the location is also good. There is the beach and you can take the bicycle to go to Puerto del Carmen or Arrecife.
Caleta de Famara
If you go to Lanzarote because of the surf, I guess you know this is the best area to stay but there are not too many more things to do. Also if you are looking for sun and beach this is not the best place because it is windy and far away.
Puerto Calero is located near Puerto del Carmen. This area is more expensive but it’s beautifully tended and quiet. There are not too many hotels and it’s an excellent area if you want to relax. In the port you can find restaurants and bout tours but if you want to go to the beach you will need to drive.