Melanie,
First of all, congratulations on your engagement and upcoming wedding!
Regarding your questions.....
Yes, this topic has been discussed here on the forum many times, and most of the group have definite opinions on each of those locations. Strictly from a logistical point-of-view, the Cinque Terre would make more sense with your Itinerary as it's easier to get to and transportation is very simple. The Amalfi Coast tends to be more posh and "glitzy" (and transportation is not always as easy) while the Cinque Terre is more informal and relaxing, a place where you can either sightsee, hike or just enjoy the occasion (and also a great place to enjoy Pesto in the area where it was invented). There are similarly strong opinions about which of the five Cinque Terre towns to stay in (my personal preference is Monterosso, but I'll offer another suggestion below).
Just to clarify a couple of points, you there are no flights that specifically go to the Cinque Terre. It's an easy hop from Florence and not all that far, so a flight would be ludicrous. Similarly, flights from Florence to Rome wouldn't be prudent as it's only a 90 minute trip via high speed train.
I'm assuming this is your first trip to Italy, and if so I would highly recommend buying and packing along a copy of the RS Italy 2016 guidebook as soon as it's available, as it will be a tremendously valuable resource in planning your trip and helping things to go smoothly.
Here are a couple of possibilities for you to consider.....
Option 1:
- Flight to Florence; 3 nights
- Train to Cinque Terre (whichever town you want); 3 nights
- Train to Rome; 3-4 nights
Option 2:
- Flight to Rome; train to Naples; private car to Sorrento; 3 nights
- Train to Florence; 3 nights
- Train to Rome: 3-4 nights
There are numerous other options possible with the places you want to visit. Which locations and order to choose will likely come down to the easiest and cheapest flights that you can find. I'm not overly familiar with flight options from Pittsburgh but I'm sure one of the others in the group will be able to provide some good suggestions.
If you decide to stay in the Cinque Terre and your budget will allow, I would highly recommend La Torretta as it's a perfect place to celebrate Luna di Miele (but not cheap). If you have room for a splurge in one location, this would be it. If you want hotel suggestions for Monterosso, post another note. One other point to mention is that Monterosso has the best beaches of the five towns.
One final but important suggestion to mention about accommodations in the Cinque Terre - BOOK EARLY! Once your dates are finalized, book as soon as possible! Note that many places are closed between Dec. - Feb. so you may not get an immediate reply.
Good luck with your planning!