There's a resort called Diamante K in Tulum, Mexico. It's quiet, really nice, not too flashy and really really romantic. You'll live in bungalows on the beach. There's even some fantastic Maya-ruins on the beach further down. And the restaurant is awesome. No more than 2-3 hours from the airport in Cancun, it's easy and no hassle to get there. Someone even told me it was the location where they had filmed some european temptation island.
My thoughts when I was there was that this was the spot I was going back to when I'm ever going on a honeymoon. It's sorta secluded, so beatiful and really romantic. And it probably won't break your budget.
Here is my own photo of the beach, seen from the Maya ruins:
