Day trip to Herculaneum from Rome

Herculaneum & Pompeii from Rome as a daytrip is certainly possible if you get an early start. The train to Naples takes a couple of hours and then you need to connect to the "local train" (Circumvesuviana). Herc will be your first stop after about 20 minutes and then Pompeii is about another 20 minutes further. They are pretty similar so after several hours you may be ready to move on. The Archaelogical Museum in Naples is also a fascinating place to see since that is where they took most of the stuff that was "portable" from the sites and put it. It's near the train station/metro stop, and is an easy place to drop in for an hour or so to round out your perspective. I would prefer to visit just one of the sites and do the museum or see the highlights of both and try to see the museum (VERY ambitious and tough to do ... I'd stop at the museum first then spend the remainder of the day at the 2 sites until they close if you're going to try that approach).

Regarding Florence as a base ... I really think it's easily worth the extra hassle of moving in order to spend at least a night and 2 days in both Siena and the Cinque Terre, as I think that is the minimum time needed to do either one justice. But to address your question, you can do Siena, San Gio and Pisa pretty easily as daytrips. The Cinque Terre is really not doable as a day trip in my opinion as you don't have direct train connections to there and you really need a chance to just linger for a while in Vernazza, Riomaggiore and Manarola. Monterosso is also pretty nice and worth a visit. Skip Corniglia unless you're there for a few days and have extra time. You can hike between the towns which is great but that's not really something you have time to do on a rushed daytrip from Florence. You can also take the trains between towns ... check the schedule carefully. We've been there a few times and as I recall the trains run about once an hour but the schedule can get a little less frequent in the middle of the day.

Florence is a great city but is very compact as for the things you'll want to see, so it is actually quite doable in a day in my opinion if you have reservations for the museums, etc. If for some reason you are adamant about staying in one place the entire time and daytripping, Lucca might be a better choice. It is a wonderful place in it's own right and is closer to the Cinque Terre.

But, my best tip to you would be to do yourself a big, big favor and stay a night (or two) in Siena (can also use it as a base for San Gio) and then move to the Cinque Terre for a night or two, stopping in route at Pisa. Pisa is a quick stop and won't take you too long (you can even see the Leaning Tower from the train as you go by enroute to the Cinque Terre).