Padua is a city where you can go walking anywhere you want.
There are people of different nationalities.
Padua is crossed by four rivers. The river Piccolo goes/runs (?) through a valley.
Fluvia is a hill near to Padua (is this ďtoĒ necessary here? no)
You are improving your marks, keep it up!
... Though I think that it'd be better if it were passive, i.e., "Your marks are improving - keep up the good work!" The agent is obvious.
Padua is a very historical city. <- change either "is" to "was" or "historical" to "historic." The difference turns on whether Padua still exists. If it does, then choose "historic", if not, choose "was."
In (the?) summer, Mars is full of tourists. You're missing a subject. I don't know what you're referring to (I'm supposing that "In the summer" is a time clause).
There are a lot of beaches, where people swim all day long (though not necessary - it just reads better with "long").
I would advise that everyone to go to Rome. (also not necessary, but I'd prefer to have the relative pronoun in this case).