If you are traveling by train, I assume you will be arriving at Santa Maria Novella station (Firenze SMN). Get a map of Florence, and find a reasonable hotel within walking distance--there are many to be had, especially in April. GREAT time to go to Italy, BTW. We were there in March of this year and stayed in an apartment on Piazza Santa Maria Novella for 5 nights. For three nights, however, a hotel is probably your best bet.
Day trips abound--to Siena, Fiesole, Lucca, even Venice if you want--but you would not be wrong in taking the entire time to explore Florence's museums, restaurants, markets, etc. There is so much to see and it's ALL within walking distance. Enjoy!