hi shelley
there is the first choice holiday village sun tropical in playa blanca, lanzarote, its AI, lots of kids activities and close to town and beach they also have apartments.
http://www.firstchoice.co.uk - not stayed here myself but walked past it and it looks nice enough.
Or there are the iberostar papagayo apartments also in playa blanca - there is a main hotel and apartments which are set across a road but connected to the main hotel with an underground tunnel. the appartments have their own pools or you can use the main hotels pools. This hotel is set outside of town but it is close to the rubicon marina (about 10/15 min walk along the seafront promenade) which has shops and bars. I have stayed here - it is a nice 4* AI.
Other hotels i can recommend are the rubicon palace - though i think their rooms are all doubles. Nice 4* AI again with 7 swimming pools!!.This hotel is also in playa blanca (hmmm there is a pattern forming here!! guess where i usually go!)
I have also stayed at the Elba sara in caleta de fuste (or costa caleta) fuerteventura which may be worth a look, there is also a AI in correljo, fuerteventura called the suite hotel atlantis resort which also has appartments and is a good standard 4* AI
Dont forget to check any hotels out on the hotel reveiw pages on this site and there is also
http://www.tripadvisor.com which is also worth a look.
fatcodycat