we will spend one day of our trip traveling from CT (monterosso) to venice and i would like to break up our train ride by stopping in one of these cities for a mid-day meal. does anyone have any recommendations?
Have been to all 3, actually ...
Bologna is a large city. I highly recommend visiting it, but a lunch stop isn't going to do it justice and the size/scale might be overwhelming if all you want is to break up the train ride.
Loved Parma! There are several streets just a few blocks from the train station that are pedestrian only and are lined with eateries. Just stroll around and pick one that looks inviting. The city center and TI office are well marked by signs. Its a much smaller town than Bologna, easier to walk around. A possible drawback compared to Bologna is that the former is a major transit hub and trains are guaranteed to stop there, not all may make the stop in Parma (or Modena).
Modena was a disappointment. The old town was a longer walk from the train station, hardly any signage directing you to the downtown area, and I wasn't that impressed with it when I finally found it. If I was doing my trip over (we were based in Bologna and did a day-trip to visit both) I'd skip Modena and spend the day in Parma.
However, having answered your question, I would suggest you consider stopping for a nite (or more) in Bologna. The region is the food capital of Italy, Bologna is home of one of the oldest universities in Europe, to me well worth a visit.
Kent points out that a stop may take more time than you think, and he's right. If I'm going somewhere I've never been before I generally figure its at least 30-45 minutes each time I change transport systems even if they are in the same building; eg. airport to train, train to subway, etc. It takes time to get oriented, find the ticket machine or booth, get to the right track, etc.
However for the specific items Kent has listed I can add 2 more pieces of information. First, Monterosso has a fully staffed ticket window. So you can buy your ticket from Parma/Bologna/Modena to Venice there. If you're taking a regional train no reservation is required, just hop on the next one that meets your timetable. For the faster trains, this would mean committing yourself to a departure time since you'll need a seat reservation.
As for finding the luggage storage, that's not going to be a problem since there isn't one in Parma or Modena! You can look at http://tinyurl.com/5fc3rg to see; at the top click on the 1st letter of the stop and you can see what services are offered at the station. You want "Deposito bagagli" and Bologna Centrale is the only one that has it. If your a RS type traveller with a single carry-on bag its not a big problem, though.
I'd probably check the train schedules to decide. When you hop off one train, there will be a wait before the next train. Find a schedule that gives you time for lunch without losing the ability to get to Venice in one day. It's a long trip from CT to Venice. We drove and ended up staying a night in Modena. I expect there will be a lot of trains from Balogna to Venice, not sure about Modena or Parma.