Hi Eagleson. not sure if you've seen this link, but it may help a little.
However, although I live in Playa Blanca... I can't work out where it is - or I'd let you have answers to your questions.
Other 4* star hotels though include the Rubicon Palace (a personal favourite), Natura Palace (comes recommended), and if you want to push the boat out... then try the Princess Yaiza (pure decadence), The Hesperia (very nice apparently, and right on the beach) erm... and there's loads more!
All of these are fairly close to the beaches.
Alternatively, why not try a villa. Angie who posts in here sometimes is a pal of mine, and has oodles of lovely ones for rent. www.lanzarotelates.com
I'm sure that others can make more recommendations on accomodation too.
Hope it helps a little.
Once you're all booked, let us know... and we can recopmmend some good places to eat and drink too. Can also point you in the way of some discounts for your stay - but I can't plug my own website... so you'll have to send me a private message for that, unless someone else posts it for me lol