Luc-sur-Mer is as good a seaside place as any other as a base for exploring the D-Day beaches, but bear in mind that it takes two hours, without stops, to drive from one end of these beaches to the other (and that Luc is toward the eastern end). You will need a car for exploration.
If you are not going to hire a car in Caen and drive yourself for D Day touring can I suggest you stay in Bayeux and take the tours from there.
Thanks for your replies, we're back from wonderful trip to Normandy.
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Definitely Caen is also a good option to stay but I would suggest if you've care then stay in near smaller towns as you can save quite a lot on hotels / airbnb. I found them 20 - 30% cheaper than staying in Caen.
I've complied lots of info in my blog from our trip last week, you can google for vikramvi knowledge sharing Normandy travel guide
Have a wonderful Normandy trip.
Plannerholic, thank for that information. Will certainly check into it as we want to do some tours and have a more charming stay.