Volcano park
Caves
Cactus garden
Cesar Manrique stuff
Vineyards
Teguise market (not my thing, but there's a big Sunday market in the town, not Costa Teguise)
Underwater sculpture museum if you snorkel/dive
watersports
boat trips to Fuerteventura/little island off north coast of Lanzarote/dolphin watching
Just looking at all the lava fields etc as you drive around
Aviation/history of tourism in the Canary islands museum near the airport.

More detail here.

We're off in mid December for sun/relaxation, will definitely be diving the sculpture museum and there's a green lake on the west coast I want to see, plus there's a little volcano above Playa Blanca, where we're staying that you can walk up and around and we'll do some snorkelling and some of the above depending on the weather/what we feel like doing.

We've been a few times but there's still loads we haven't seen as there's so much more to Lanzarote than laying round a pool drinking.

There is loads to see in Lanzarote. BarbaraofSeville has given you an extensive list, most of which we have done, and is definitely worth doing. IMO the unmissable ones are Timanfaya National Park and the Cesar Manrique sites.
We stayed in Costa Teguise one February half term, and it was quite chilly. The wind didn't help.

CostaTeguise doesn't really have a centre, nor does it have a harbour. I really liked Lanzarote, but found Costa Teguise a bit devoid of any character, so I would go with realistic expectations of the resort.

Loads to see and do but take a wind proof.