hey hey daniel
where are you flying in from USA, Canada, another place in europe, etc? is it only you and girlfriend coming in early before the wedding and traveling by bus or train? september is a busy month to travel with harvest season, conferences, good weather most of time, some think back to school with families that have spent summer time, locals back at work that took august off. it's still high season with higher prices. will you be renting a car, if so you will need an IDP (coincides with driver's license) from AAA/CAA for about $25 and 2 passport photos for each driver, good for one year.
we all have different opinions of what to see/do, what's important to you, where to go and spend time. being your first time to italy, "we" all want to see everything but 6 days is not a long time. first night could be jet lag, roam around looking, not standing in lines for hours to get into an attraction, make sure you reserve ahead of time, skip the line does not mean skip security lines. there is no right or wrong with what you plan. people here will help and give you good bad and ugly, you decide from there.
do a multi-city flight, into one city out from another. i agree with a few people here to fly into rome and out of florence/pisa or fly to milan for 2 days train to venice for 3 nights then train to florence for wedding, fly out of florence/pisa.
others have said not spending time in cinque terre where it is overcrowded with cruise passengers and day trippers. cruisemappers.com lets you look at how many ships are in port that day, if you have 4 ships that's like 20,000 people not counting day trippers, waiting for trains that are so crowded they pass right by you. not my cup of tea.
with your 4 days for wedding and activities, are there plans to see cities/villages of tuscany, wine tour, place to stay is same as wedding venue, florence day trip, how many people are planning to attend?
seat61.com is all train travel
know your flight arrival times to check in hotels usually 2-3pm, early check-in or luggage storage. stay in a hotel that you can ask questions within city center. you have a lot of time to research, what's important to see and do, what flights are available that suits your fancy. ask questions to get answers to make things much easier and planned out when you get there, you'll be much happier. enjoy