I've never used public transportation when in Italy (I've only been to Rome, and literally walked EVERYWHERE there!). This trip I'll be traveling to Milan (from Switzerland), Vernazza, Florence, Bologna, then Padua, with lots of day trips planned, so I expect we'll become very familiar with trains.
Thoughts?
Maybe you could tell us where your hotel is and we could give a recommendation. There is a tram that runs by the train station through the center of the old city to close by the Basilica of St Anthony, by the Prato della Valle and on south. You can buy tickets at the TI that is located in the station building out the main door to the right, as well as other local info. There is a 2 or 3 day tourist card that gives a lot of free and reduced entry fees at sights, plus unlimited use of local public transit.
http://www.turismopadova.it/en/context/423
I stayed in a hotel near the Basillica d'Santantonio. I could have taken the tram and then walked. I took a cab. Door to door. 8 Euros and change (on the meter).
However, don't be afraid of public transit.
I'm staying at AC Hotel by Marriott Padova, Via Prima Strada, 1, 35129 Padova PD, Italy
Your hotel is sort of on the outskirts of town You could take the U10 bus from the train station to your hotel. It stops about 500 feet from the hotel.
But, I would still take a cab and let your hotel teach you about using local public transit.
Take the taxi anytime you travel with luggage (I.e. when you first arrive or depart).
Once at the hotel, ask the staff about city bus options, if your hotel is not in the city center, like in the Padua case. If you are in the city center, chances are you will rely on your feet.
Trains are simple to use. I presume that for Day trips you will be taking Regionale trains. Regionali are commuter trains. Once you buy the ticket to your destination, you must ensure you validate the ticket (date stamp it) before boarding. From the time of validation, you must complete the trip within 4 hours, generally (6 if over 200km away, I think).
Below is a video on how to purchase train tickets at the automatic kiosks (which usually have no lines, unlike the ticket office) and how to validate the ticket before boarding. The video was filmed at Firenze Santa Maria Novella (Florence main station), my old stomping ground.
Padua is a great base for day-trips. Among the easy ones are Vicenza, Verona and Ferrara.
I suggest stopping at the tourist office before heading to your hotel. Check on the tourist card, make a reservation for the Scrovegni Chapel if you haven't already done so, and find out where to pick up some bus/tram tickets if you decide not to go with the tourist card. You don't want to be out at your hotel without bus/tram tickets, assuming you can't buy them on the bus/tram.
