Quick answer: Rome runs about EUR 120 per day mid-range - noticeably less if you eat local and walk. Cheapest window: April-May and September-October - warm but not scorching, and thinner crowds than midsummer.
What things actually cost
espresso at a bar (standing)
1.20 EUR
pizza margherita in a trattoria
9 EUR
metro or bus single ticket
1.50 EUR
Colosseum standard entry
18 EUR
glass of house wine
5 EUR
gelato (two flavors)
3 EUR
Eat well for little
Cacio e pepe in Trastevere - pecorino and black pepper perfection, about 12 EUR a plate
Pizza al taglio at Bonci Pizzarium near the Vatican - sold by weight, about 5 EUR for a filling slice
Suppli (fried rice balls) from a friggitoria - the classic Roman street snack, about 2 EUR each
Carbonara in Testaccio - the neighborhood that claims to do it best, 12-14 EUR
Gelato at a shop that covers its tubs (a quality sign) - about 3 EUR for two flavors
Money mistakes to avoid
Not booking the Colosseum, Vatican and Borghese Gallery in advance - same-day tickets often sell out or mean 2-hour lines
Eating at restaurants with photo menus next to major sights - walk 5 minutes into a side street and prices drop by a third
Cramming the Vatican and the Colosseum into one day - they are on opposite sides of the city and each takes half a day
Forgetting to validate paper transit tickets in the yellow machines - inspectors fine on the spot, around 50 EUR
Transport without the tourist tax
From Fiumicino, the Leonardo Express train reaches Termini in 32 minutes for 14 EUR. The center is best on foot; the metro (single ticket 1.50 EUR) covers the gaps to the Vatican and Colosseum.