It is a very interesting island especially where there are the latest eruptions. The beaches and the sea are beautiful.
See it!

Hi Moon

I'm sure you know that Sun Beach is relatively close to the town centre and so is an easy walk in to town and also nice and easy to walk to the lovely Marina rubicon. For entertainment there is CC Papagayo just behind the Dorada beach (literally at the end of the road for you) which has live music bars, karaoke bars, cafes, restaurants nice and close - if you go to Marina Rubicon in the large shopping centre there is 10 pin bowling and a mini-golf and behind the harbour (other end of town centre) is CC Punta Limones also with some live music bars and karaoke bars as well (also the towns only Fish & Chip restaurant).
On Dorada beach there are plenty of activities including para-sailing (towed behind a boat in a parachute), banana boats, pedalos, jetskis, kayaks and other watersports - along the promenade in Kikoland is a football school for fun and skills - in CC Papagayo is "Hubs & Tubs" a new bike rental place with some very cool pedal karts as well as bikes and by the harbour is "Electrobike" with electric bike rental (to take you further). There are plenty of dive schools, personally I dive with Marina Rubicon diving and they have a new English instructor Rich who as an ex-teacher is very patient with new people learning.
As for the car-hire if you really do want to not visit anywhere in your first week (are you really sure?) then it will be cheaper to hire it for a week - autoreisen or Felycar (in resort) are good places to start for pricing!
To go to a "drag" show you will need to go out of the resort as there isn't a drag show in Playa Blanca many different tributes in lots of the bars and even a fantastic snake show! I'm sure you will have the most fantastic of holidays!

Santa Barbara Castle on a volcano near Teguise hosts a museum of the history of the Canarian people. Very interesting to find the links to San Antonio in America etc, also spectacular views.
The Agricultural Museum in Tiagua, showing what used to be a working farm with wine tasting and tapas.
The Tanit museum in San Bartolomé, an old style house.
The antonio padron art museum in Tías.
Lanzarote Aquarium in Costa Teguise........

How long you on the Island for???