There are a few general principles about travel planning in Italy.
Trains are often faster than driving; fast trains are really fast along the railway backbone (Milan-Bologna-Florence-Rome-Naples), along the axis Turin-Milan-Venice, as well as on the Venice-Bologna-Florence-Rome itinerary (that makes use of the longest part of the backbone). Out of this main line trains are slower. If you join arbitrary points in Italy you are likely not have very fast travel time.
Cinque terre and Venice are on opposite sides of Italy, and in the middle there are very boring mountains, a lot of them. If you manage to do it in five or six hours by train, it is still a miracle of railway building. Twenty years ago it would have been eight hours. Still, six hours traveling means the better part of your day is gone.
Rural Tuscany - and that includes S. Gimignano, Pienza, Montepulciano, is difficult to travel with trains. Even with a car it is not fast driving. You will have to climb every hill and turn around every field. - Tuscany is nominally possible with buses, but timetables are planned for students and not for tourists. Very very slow.
Dolomites begin at Ortisei - that is not on a train line but still a feasible bus ride from Bolzano. The interesting part would be to ride passes and get really in the internal zone of Dolomites. This needs time, a car, and good weather. Usually planning to spend a single day or two in mountain areas (be it Dolomites or Berner Oberland, whatever) it is not sensible planning; your single day may be cloudy and all your travel time is lost. Three days in a mountain area are a sensible minimum, if you do not have you should better skip the area (but even a full week is not a guarantee that weather will be fine).
Basically, you need time for everywhere, unless you stick to the railway backbone. On the railway backbone, I can get up at 7am, leave at 8am from Florence, have a meeting in Milan at 11am, go back by train at 12.30pm, and be in front of my dish of spaghetti in my home again at 2.30pm. Out of the backbone, forget to do many things on the days you travel.
The last principle: relax. The best of Italy is having little or nothing to do in a nice place in front of a bottle of wine - if you do not drink, in front of something good to eat. But you need time just to enter into this mindset. Most tourists are already gone before being ready to relax.