Caffè Pedrocchi
Via VIII Febbraio, 15, 35122 Padova PD, Italia
Since 1916 it used to be open day and night and, for this reason, it was known as "caffè senza porte" (the coffee place without doors). Today it is one of Padova's land marks, it is still active and it has a room where you can enter and sit without having to order or consume anything.

La Gineria
Via Francesco Squarcione, 4, 35122 Padova PD, Italia
If you are looking for a place where to get a cocktail, La Gineria is what you are looking for. Just note that, at times, the service can be a little slow, so don't go there in a rush.

Box Pizza
Prato della Valle, 19, 35123 Padova PD, Italia
This restaurant is small, but incredibly good. If you decide to dine here, I suggest you try "pizzette fritte", which are small fried pizzas which they serve as an appetizer.

Dalla Zita
Via Gorizia, 16, 35139 Padova PD
If you are looking to have a sandwich this is the best place in Padova to get one. The place is microscopic and there can be a cue, but just know it is fast. The menu is displayed on the wall to your right as you get in. The wall, which is covered in colorful cards, each represent a different sandwich. Take your time in reading all the options, but whichever you decide to choose it will be great. Among my favorites are: Elisa, Lisbona and Olandese.

What can't be missed:

Cappella degli Scrovegni
Piazza Eremitani, 8, 35121 Padova PD
This chapel hosts the frescos by Giotto. You will have to book your visit, but it is breathtaking, so I highly reccomend you do not miss it! Before you enter you will be shown a video which introduces you to the history of the chapel.

Battistero del Duomo di Padova
Piazza Duomo, 35139 Padova PD
The interior of the Battistero is covered in frescos by Giusto de’ Menabuoi, if you wish to visit it I suggest you do so before visiting the Cappella degli Scrovegni as otherwise the comparison will be less impressive.

Chiesa degli Eremitani
Piazza Eremitani, 9, 35129 Padova PD
Not many people know that in this church you can find the frescos by Mantegna.

Notes and Suggestions:

Padova is said to be "la città del caffè senza porte, del Santo Senza Nome e del Prato senza erba" [the city of the coffee place without doors, the Saint without a name and the lawn without grass]. The reason behind this is because Caffè Pedrocchi has a room which you can access even without consuming, the Basilica di Sant'Antonio which is the city's main church is affectionately called "Santo" by locals cutting it's name and finally, Prato della Valle that today is covered in grass used to be stone-covered (prato in Italian means lawn).

Padova is one of Italy's streetart capitals, among the various artists you can admire on some walls in the city center you can find Kenny Random, Alessio B. and Tony Gallo.

Suggestions to dine outside the city center:

Senza Spiga
Via Brentella, 25, 35030 Selvazzano Dentro PD
This is a great option for celiacs who are looking for places dedicated to them near Padova.

Antichi Sapori Vigonza
Via Leonardo da Vinci, 4, 35010 Vigonza PD
Antichi Sapori has, in my opinion, the best pizza in Padova, this is the pizza Napoletana, which is higher than the one you usually find in Northern Italy.