Quick answer: Edinburgh runs about EUR 150 per day mid-range - noticeably less if you eat local and walk. Cheapest window: May-June and September - mild weather and long daylight without August festival crowds (come in August only if you plan for the Fringe and book far ahead).
What things actually cost
flat white at a cafe
4 EUR
pint of ale in a pub
6.50 EUR
fish and chips
11 EUR
Edinburgh Castle entry
23 EUR
bus day ticket
5.80 EUR
mid-range dinner main
18-22 EUR
Eat well for little
Haggis, neeps and tatties at a traditional pub - about 14 EUR
Full Scottish breakfast - about 12-14 EUR
Fish and chips - about 11 EUR at a proper chippy
Hog roast roll from Oink on Victoria Street - about 7 EUR
Whisky flight at a specialist bar - about 15-20 EUR for three drams
Money mistakes to avoid
Arriving in August without bookings - Fringe month doubles or triples room prices and sells out months ahead
Never leaving the Royal Mile - Dean Village, Stockbridge and Leith show the city locals actually live in
Packing for one type of weather - you can get sun, wind and rain in an hour, bring layers and a waterproof
Renting a car for the city - parking is scarce and expensive, and everything central is walkable
Transport without the tourist tax
From Edinburgh Airport the tram or Airlink 100 bus reaches the center in about 30 min for roughly 5-9 EUR. The center is best on foot - it is hilly but compact - with Lothian buses (about 2.30 EUR single, 5.80 EUR day ticket, contactless card works) for longer hops.