Padua is easy to get to by high-speed rail from Florence or Milan.  A local train from Venice takes about half an hour.

The hotels I recommend staying in Belludi 37 (more luxurious, no elevator though), the budget M14 (stay away during student vacations however), and the small family run Albergo Verdi.

For 16/21 euros purchase a 48/72 hour Padova card for unlimited public transportation on public bus and tram and admission into the major sites of Padua.

Here are the top sites to see in Padua:

Scrovegni Chapel:   Giotto's frescoes have been restored and are vibrant and exciting.   Better than the Sistine Chapel?  You be the judge.

Basilica di Sant'Antonio da Padova:  The bones of St. Anthony lie in this marble chapel with sculptures and ornamental decoration.

Caffe Pedrocchi:   Reminisce in one of the most beautiful cafes in Italy.  Make sure to visit the residence upstairs.

Cornara Loggia & Odeon:  One of the best examples of Renaissance architecture.

Ragione Palace:  One of the largest halls and most beautiful structures in Italy.   In the morning visit the downstairs market and vegetable market in the adjacent square.

University Tour:  Not on the Padova card, sign up in advance to get a look at the famous university where Galileo spent the most satisfying years of his career.

Padua has squares and markets that make this a delightful walking city.   The Jewish ghetto is unique, filled with small shops and boutiques.

I think because of its large student population, traditional sit-down restaurants are less popular than cafes.  However, I recommend Ristorante Zairo for a wide variety of dishes in a wide-open bright atmosphere.   Near the Ragione Palace check out family owned al Peronio for a hearty, authentic meal with dishes made from local produce.