I will preface this by saying that I have not been to Bonaire or Turks and Caicos, but T&C is eventually on my list. If what you loved about LC was how effortless the diving was, you might want to look very carefully at what you are paying for on Bonaire before deciding to go that route. Shore diving on Bonaire has many similarities to LC, in the form of shallow dives, mostly easy currents, no "follow the leader" divemaster parade, etc. But it also has what LC does not...carting your gear out to the truck, driving to a dive site, carrying your gear down to the water, carrying your gear back to the truck after the dive, driving back to your hotel, rinsing out your own gear, getting stuff stolen from your truck if you leave anything of value in it, leaving your hotel to find a good restaurant, paying for the food, etc.
At least to me, what makes LC such a relaxing experience is that you don't have to do any of that. You show up at the boat, setup your gear once, and after that, you don't mess with it for the rest of the week. You don't have to decide what restaurant to go to, you don't have to decide how much you are willing to spend on food each night, you don't have to worry about stuff getting stolen, you just dive, eat, relax, and sleep. If that is what you loved about LC too, then maybe Bonaire's shore diving isn't what you are looking for.
I think those kinds of experiences are pretty rare in the rest of the Caribbean...and where they are, they are not cheap. I have looked at Small Hope Bay on Andros as an option, haven't pulled the trigger due to air connection issues trying to get there from Houston. T&C is in the same boat for me...not as easy to get to, but on the list of places I want to try, although as a committed air hog, I am worried that I won't enjoy T&C as much because I will be forced into shorter dive times. The Belize atolls can be good, but frankly, I wasn't as impressed with the diving there...same with Roatan. It is good, but just not the same level of variety in the terrain and health of the reef that we are used to on LC. And it is getting obscenely expensive to fly to Roatan these days. Now that TACA isn't having to compete with anybody and United is content to make their price whatever TACA wants to charge, it is hard to get there for less than $700 RT.
But in the end, don't take our word for it...as you can see, there are lots of different opinions out there and the best way to see if you like a place is to go try it yourself.