I would say the one place not to miss is the Timanfaya National Park (the Fire Mountains). If you choose to hire a car, I would suggest getting one for three days. That would give you a day to explore the south of the island, a day for the north, and then use it on the third day to revisit some of the places you passed through on your way to the sights! Enjoy your hols!!!

HTH

Were do you start. Firstly, fully endorse madsue's recommendation - hire a car - at least 3 days. Then........

Lanzarote
I think it has much more to offer the tourist in places to see.

Places to Visit
Cesar Manrique House. Fantastic house built around a lava flow. Has wide bright rooms full of art work and a beautiful garden. Well worth seeing.

Jameos del Agua (Caves) - well worth the visit. Created by Cesar Manrique and so easy to explore using the subterranean walkways. Once you have paid the entrance fee you are then left to spend as long or short a time as you require and browse the cave in your leisure. The pathway down leads you to a nightclub area that is open three nights a week, and then onto a large underground lake that holds albino crabs, after this you go through a narrow walkway along the right hand side of the lake that leads you to another small bar area and then up into the open air section. Here is the swimming pool that only the King of Spain is allowed to swim in. Steps then lead up to a terraced area with a small cafe and a Volcanic Museum. There are plenty of opportunities for photographs and areas to sit and just take in the surroundings.

Las Cuevas de los Verdes (Caves) - they are part of the same system as Jameos del Agua and again a must see. These are natural lava caves that you go through with a guide and this takes about 45 - 60 mins, depending on the group size. Our group was about 20 strong and this was a good size because all the explanations are done in Spanish and English if there was any more it would be more difficult to see and hear. Because these are volcanic caves you can see how the lava flowed on the side walls and they have also used lighting to emphasis the main areas. The main feature of these caves is a secret area that will be shown to you by the guide so I will not enlighten you any more on that. Again, plenty of opportunities for photos and just a small warning in places mind your head you will have to duck to go through some of the areas. No Health and Safety here.

With both of the above they are busy and because the Las Cuervas caves have a guided tour I suggest that if you are pushed for time you do these first. The caves are about a mile apart.

Timanfaya (Volcano)
If you decided to include this can I suggest you try and sit on the right hand side of the coach, better views. At the end of the coach tour you can then visit the displays of heat. After which a visit to the restaurant for a drink or some food, hot food after 12 noon (cooked by the Volcano's own heat) and then a visitors shop.

Guinate Tropical Park - a little further afield and there is lots to see here, especially for the children. Parrots, Toucan, Ostriches, Tortoise, Monkeys to name but a few. There is a Parrots show also, three times a day. Worth a visit About 1 hour from Arrecife.
Mirador Del Rio (viewing point) - a little further along from Guinate Tropical Park with spectacular views over La Graciosa island and the entrance fee also allows you a free drink. About one hour from Arrecife.

Los Hervideros; The rugged coast line just along the coast from Playa Blanca. Large caves formed by the crashing of the sea. Walkways along the top and partly inside with viewing platforms.

El Golfo (green lake) - Large lake cut off from the sea many years ago. Now turned a bright green. If you do visit and want lunch can I suggest the La Lopa restaurant, first restaurant on the right as you approach the main village. Excellent service and very reasonably priced. Can I recommend the Canerian stew and filleted catch of the day, served with Canerian Potatoes and Mojo sauce.

Yellow Submarine: This goes from a small marina just outside Peurto del Carmen. It was a little expensive, but well worth the trip. Lots to see, your own porthole, not cramped, diver outside to attract the fish.
This is a link to some photographs of Lanzarote.

http://picasaweb.google.co.uk/PeterJD01/Lanzarote#

- Mirador del Rio on the north of the island ; it is a popular view point (500 mt. altitude) with a restaurant worth to visit.

- La Graciosa Island ; good for a daily visit

- Cactus Garden on the northern Costa Teguise

There is so much to see in Lanzarote - all of the places mentioned are great, though we haven't been to the Yellow Submarine yet! Top of my list would be Fire mountains and Cesar Manrique house but also love Mirador del Rio, Cactus Gardens and Jameos del Agua