There are some nice hotels in Lanzarote, many of them quite new, but at that time, you should be aware that Costa Teguise is a little windier than Puerto del Carmen or Playa Blanca
That said I like the Occidental Oasis- In Teguise especially if it's for a family holiday. It has lovely rooms, great swimming pools and it's on the beach. The standards are high and I've had many clients go there over the years with no complaints.
I also like The H10 Rubicon Palace in Playa Blanca, it's been a favourite for years and is well-worth a look, but check the prices carefully as it does vary quite a bit. It might be best to book flights and accom seperatley for that one. And theres also the Papagayo Arena which is ok too.
there are a couple of Iberostar Hotels in Lanzarote- a cheaper one is usually Costa Calero, but the resort is under development and theres not a lot going on. It's also quite a way from the airport so bear that in mind, but if you stay in the hotel once you're there and you don't look at the building work, you'll be ok!
Puerto del Carmen is the closest to the airport and less windy than Teguise but avoid The Green Oasis Lomo Verde- it's apartment style accomodation and not great.
Actually, theres not much in the way of decent AI in PD Carmen, and if you want to be in that resort then I'd suggest HB/FB at The San Antonio, The Fariones or if you still fancy youre AI then try Playa Poccilos at the Riu Paraiso Riu hotels are always pretty good.
Theres a lot of AI in Lanzarote, so there is a good choice, but the best in my opinion is The Occidental Oasis and I'd go there if I were you if it really had to be AI- But... just to confuse you even further, theres also The Princess Yaizza in Playa Blanca HB or The Fabulous DreamPalace also in Playa Blanca. Only HB though but oh so lovely!
Wherever you go, I hope it goes well for you.