Quick answer: Madrid runs about EUR 125 per day mid-range - noticeably less if you eat local and walk. Cheapest window: March-May and September-November - sunny and mild, July-August afternoons are punishingly hot.
What things actually cost
cafe con leche
1.80 EUR
cana (small draft beer)
2.50 EUR
menu del dia lunch
13 EUR
metro single ticket
1.50 EUR
Prado Museum entry
15 EUR
churros con chocolate
6 EUR
Eat well for little
Bocadillo de calamares near Plaza Mayor - 4-5 EUR, Madrid's fried squid sandwich ritual
Menu del dia (three-course set lunch with drink) - 12-15 EUR at neighborhood restaurants on weekdays
Churros con chocolate at Chocolateria San Gines - about 6 EUR, open since 1894
Cana plus free or cheap tapa in La Latina - 3-4 EUR per stop, crawl instead of one sit-down
Cocido madrileno (chickpea stew) - 15-20 EUR, a heavy winter classic served in courses
Money mistakes to avoid
Showing up for dinner at 6pm - most kitchens open around 8:30pm, do a menu del dia at 2pm like locals instead
Paying full price at the Prado - it is free the last two hours Monday to Saturday evenings, just expect a queue
Basing yourself right on Puerta del Sol - noisy and overpriced, Letras or La Latina are minutes away and nicer
Cramming all three big museums into one day - pick one per day and pair it with a neighborhood
Transport without the tourist tax
From Barajas Airport take the Cercanias C-1 train (about 2.60 EUR) or the 24/7 Airport Express bus (5 EUR) to the center in around 30-40 minutes. The metro is excellent - singles cost 1.50-2 EUR and a 10-ride Metrobus pass about 12 EUR.