Big Lou;
If you just got certified in the past year (as have I - February for me) I am gonna assume (yes I know what risk that carries) you haven't had a chance to dive all that much yet (I just got #21 last weekend - yay me!). I will then further assume that you're interested in the same things I am... pretty colors, lots of life, neat stuff to look at...
I would recommend going down to Key Largo and hooking up with Horizon Divers (great operation, and one of the most inexpensive down there) when they do a dive on the City of Washington.
It is a wreck of a wreck really, just some twisted metal and whatnot, but...
A: it is covered with growth and surrounded by coral growth just a short swim off of the wreck, and...
B: some outfit (I don't know the name and wouldn't patronize them if I did) feeds the fishies on the wreck and takes pictures for the tourists.
So there are always lots and lots of nurse sharks swimming around (I think 8 last time I was there), the occasional reef shark (saw 2) and a "resident" jewfish (goliath grouper) who's almost as big as my loveseat.
As I said, I have only had 21 dives so I am definitely not a font of knowledge by any means but this was my fave dive yet. I think it around 30fsw so you get lots of bottom time. I think it's awesome and the nearby reefs don't suck either.