firenze
How to get
The Department of Mathematics and Computer Science "Ulisse Dini" is located in viale Morgagni 67/A (how to get, gmap, osm). The nearest tram stop is Careggi Ospedale for tramline T1 (tramline). The nearest train station is Firenze Rifredi (Trenitalia). You can also use local bus connections (ATAF, moovit).
If you are lodged at Residenza Marotta, it is located in viale Taddeo Alderotti 89/A (gmap, osm), five minutes walking from the Math Department; the nearest tram stop is Morgagni Università for tramline T1. If you are lodged at Il Guelfo Bianco, it is located in the city center, via Cavour 29 (gmap, osm); you can reach the main train station SMN and the tramstop Unità for tramline T2 by walking in ten minutes, or use the bus stops in Piazza San Marco.
If you are lodged at my place, you first reach the Math Department or the tram stop Careggi Ospedale for tramline T1: my house is around 25 minutes walking distance.
The tramline connects the city center (where the station Santa Maria Novella) with the airport and with the northest part of the city (where the Math Department). You can buy tickets at the vending machines at each stops, for 1,50 euros; stamp it when on the tram. From the airport to the downtown: at the exit turn left, take tram line T2 toward Unità and get-off at Alamanni Stazione or at the last stop Unità, in around 20 minutes. From the city center to the Math Department: take tram line T1 from Alamanni Stazione or Stazione Valfonda towards Careggi Ospedale, getoff at the last tram stop Careggi Ospedale, in around 20 minutes. At the airport, you find a taxi on the right at the exit, cost is between 15 and 20 euros to reach the Math Department or the city center; the phone number is 055 4242.
What to see
Giardino delle Rose and Giardino dell'Iris are wonderful gardens near to Piazzale Michelangelo, where you can enjoy a beautiful view on the city. Another quiet park is Giardino dell'Orticultura (near Piazza della Libertà).
Near the Math Department, you can find wornderful panini at Na'nticchia! Try also Alimentari Bruscoli or Il Tempio del Panino.
Some good places for pizza: Gustapizza (in Santo Spirito: you can take away and eat outside in the square), Cucina Torcicoda (near Santa Croce), Da Gherardo (in San Frediano), Da Michele (near Mercato Centrale), Vico del Carmine (in San Frediano), Pizzeria Le Panche (near the Math Department), Pizzeria 00 (in Statuto, not far from the Math Department).
You can find a true coffee at Mo Sì (near the main station, Neapolitan style: try sfogliatelle!) or Pasticceria Baratta (near the Math Department, Sicilian style: ask for cannoli!!).
The library called Oblate is near the Cathedral: you can work there until late and on saturday, or just take a beer with a wonderful view on the dome. You can enjoy a beautiful view also from Caffé del Verone at the top of Istituto degli Innocenti (in the wonderful Piazza della Santissima Annunziata).
Other wonderful place for co-working is Todo Modo, and also Sit'n'Breakfast. Another good place for beer and apericena is Le Murate (not far from Santa Croce). Other good places for drinking and eating are: Mosto Dolce (near the main station), Café de Paris (in Piazza Dalmazia), La Farmacia dei Sani (in Piazza Giorgini), Il Conventino (near Piazza Tasso), Fast Sud (near Piazza della Libertà, Souther style), Vino e Ravioli (near Stazione Leopolda, a mix of Abruzzo and China style). For drinking: Il Santino (in San Frediano), Pin Up Café (in Piazza Dalmazia), Sabor Cubano (near Mercato Centrale). If you want to take a beer and play foosball, go to Circolo il Progresso (near Piazza Giorgini)!
Some suggestions on restaurants: La Cucina del Ghianda (near Santa Croce, where you can find also typical food from Lunigiana - approved by a local!), Trattoria Da Ruggero (near Porta Romana), I' brindellone (near Santo Spirito, for Fiorentina steak), La Mangiatoia (near Santo Spirito), Trattoria Sabatino (in San Frediano), la Bottega della Nonna Nina (in Serpiolle, call in advance), La casa del prosciutto (near Fiesole), La Bottega di Monte Morello (near Monte Morello), Il Focolare (in Montespertoli, for a very good Fiorentina steak!). More suggestions for the Fiorentina steak in the city can be found here.
The best gelateria in the city is a matter of long debate: I would suggest Gelateria La Passera (near Santo Spirito), Gelateria de' Medici (in front of Statuto tram stop for tramline T1), Dona Malina (in Piazza Dalmazia, and also in San Jacopino), Gelateria Dalmazia (in Piazza Dalmazia).
As for seesighting. The entrance to the Cathedral is for free, and the queue may be long. To climb the Tower of Giotto and the Cupola, you need the same ticket as for the Old Cathedral and Museum and Battistero: book the entrance at least three days before online. Same for Uffizi; see also Corridoio Vasariano. Other suggested itineraries: Santa Croce, Ponte Vecchio, Piazza della Signoria, Piazzale Michelangelo and Abbazia di San Miniato al Monte; Palazzo Pitti and Giardini di Boboli; Galleria dell'Accademia, Museo Stibbert, Museo del Bargello. In the area around my house, there are some Ville Medicee with wonderful gardens: Villa di Castello (hosting Accademia della Crusca) and Villa Petraia (see also here, hosting Giardino Farmacia Santa Maria Novella); to visit, keep informed on the timetable and book by email the free tours.
There are many free walking tours to learn about the city.