well, its abit of a problem...
yes there are really nice diving sites in the med, in isreal, but, and it is a very big but, good diving days are rare... we say that in the med you dive when ever you can, not when you want to.....
as for sites, you have the "shira" an italain sub, from wwII, in haifa. 40 min from ceasarea.
you have the "kidon" an israeli missile ship, sunked as a memorial site for the israeli naval commando, an hour north of ceasarea.
and many more, i'm just more into free diving, so i take my bike and go to the nearest beach (400 m) to my house..
about intros, im not sure but i think they can do it..
as a matter of fact very few israelis dive the med so who ever gets there, welcomed.
as for the red sea, i DO NOT recomend diving in eilat!!! if you want to dive the red sea, go to sinai, its a LOT better and a LOT cheaper!!! eilat is all packed with divers, i dont bother to wet my gear down there....
if you do get nice days in the med its lots of fun!! in the winter you also get good days but its a little bit cold (16-17 c)
well i hope i'v been usefull...
enjoy israel anywas!!!
if you will dive ceasarea, dont miss the "Helena" restaurent right next to the diving center.... you won't regret it.