The area right at the train station wasn't my favorite part of Padua. I wouldn't stay there, especially not for a week, but you might have a different reaction. You might try walking the streets nearby on Google.
The city has a tram line that passes the train station. A hotel near one of the other tram stops would be convenient since you'll be doing day-trips. Take a look at the Google map. Zoom in as necessary. The core of the old town is sort of peach colored and partially enclosed by the river. You'll see Palazzo Bo in the middle of it. A bit north are the Eremitani Church and Scrovegni Chapel. Just a bit beyond them is the main station, labeled simple "Padua" [oops--Google uses the Italian form, "Padova"].
I enjoyed wandering all over the historic district. I think I even crossed the little branch of the river you see to the south. I wasn't paying attention to hotels, though.
There are markets on one or both of Piazza delle Herbe and Piazza della Frutta. They might be noisy in the morning and not good places to stay, but Google isn't showing any hotels there, anyway.
Sorry not to be more help. The hotel I used--where the air conditioning was either broken or turned off for my entire stay--has since closed. Not shedding any tears about that.