Hi, I live in Valencia. I'm assuming that you're going to hire a bike or do you intend to drive?
Actually it's academic, really, as I have some bad news for you; you're better off not bothering.
Firstly, it will likely be too hot and humid for a decent ride unless you like riding in shorts and t-shirt. I guarantee you will not enjoy a ride in anything else, much less in full gear. However, if you're going to hire a moped or a scooter, then you can ride in shorts and t-shirt and the coastal road will offer nice views and a winding road all the way to Calpe (for instance).
Secondly, most of the decent rides require you to travel some distance away from Moraira in rder to find them.
Thirdly, this really is not the time of year to be riding, or indeed, driving, around that area because of the traffic. Those same roads from October - April are...... OK (still never great, though), but in the summer very busy.
It's the heat, though, that is really the thing that will put you off; after an hour you'll be asking yourself why you bothered when you could be lounging by the pool or sipping a cold one in "El Portet".
My advice: Enjoy your week of sun, sea, sand, beers and calamari and forget going anywhere.