[Edited to add: Lola's suggestion of Ferrara is a good one; time-wise, it works better that Bologna if you must go in both directions from one base. It's still more travel time than I'd want if I planned three day-trips over the course of six or seven days.]
I don't really think there is a place that works for visits to both Venice and Modena/Parma. You won't want to spend 5-7 hours a day on trains. Keep in mind, too, that it's not just the train time you need to budget for; you also have to get back and forth between your lodgings and the train station, plus time to find the right track, which can add considerable time in each direction.
Italy has some very fast trains. The Frecciarossa, Frecciargento and Frecciabianca trains will whisk you between large cities extremely fast, but they do not stop everywhere. For trips of any distance, it's advantageous not to need the much slower regional trains that serve small towns. It's also important to check how long a layover you'll have if you need to transfer. A couple of 45-minute layovers add 1-1/2 hours to total transit time.
Parma and Modena are easy; they're close to each other and on the same rail line. Venice is the outlier. To side trip to both Venice and Parma/Modena, you'll need to change trains in Bologna unless you choose Bologna itself as your base. That's where rail lines to Venice and to Modena/Parma meet.
Bologna has a lot to recommend it. It's a great food city with one of Europe's largest medieval centers. I believe there are food tours operating from Bologna to Modena and Parma, as well. The complicating factor is that the main train station in Bolgona--from which you'd be taking your day trips--is quite a walk from the historic center, the best place to choose a hotel. Google Maps tells me the Piazza Maggiore is about 0.9 miles from Bologna Centrale RR station. By the time you walked to a bus stop and waited for a bus, it might not be much faster than walking the entire way.
And the fact is that even the optimum choice (Bologna) means over 3 hours round-trip on the train to Venice--with really significant walks on both ends of that rail trip; I'd figure on about 5 hours in transit for that trip, which puts you in Venice during the same horribly crowded mid-day hours when everyone else is there. That's not the way to see Venice. You can explore travel times on the Trenitalia website. You'll need to use the Italian station names, as follows:
Venice: Venezia S. Lucia
Bologna: Bologna Centrale
Padua: Padova
Parma
Modena
Vicenza
Don't forget to change the time of day for each search, and note that schedules vary by day of week, especially for Sunday.
In case it helps, here's schematic map on Trentitalia's routes. There are others out there that may be easier to read. I really can't see the difference between the heavy blue lines and heavy green lines on my monitor.
Trenitalia rail schematic
I believe you should either defer Venice until a later trip--which could also include Padua, Vicenza and Bassano del Grappa--or spend some nights in Venice and some nights in the Parma/Modena area.
