Quick answer: Seoul runs about EUR 90 per day mid-range - noticeably less if you eat local and walk. Cheapest window: April (cherry blossom) or October (autumn).
What things actually cost
subway ride with T-money card
1.10 EUR
street-food snack (tteokbokki or hotteok)
2.50 EUR
specialty cafe latte
3.50 EUR
Korean BBQ dinner per person
12 EUR
Gyeongbokgung Palace entry
2.20 EUR
taxi base fare
3.50 EUR
Eat well for little
Samgyeopsal (pork belly BBQ) grilled at your table - budget 10-14 EUR per person with sides and soju
Bindaetteok (mung bean pancake) at Gwangjang Market - fried fresh in front of you, about 4 EUR
Kalguksu (knife-cut noodle soup) at Myeongdong Kyoja - filling bowl with endless kimchi, about 7 EUR
Tteokbokki (spicy rice cakes) from a street cart - the classic snack, 2-3 EUR a portion
Chimaek (fried chicken and beer) in Hongdae - a whole chicken to share runs 14-18 EUR
Money mistakes to avoid
Not loading a T-money card on arrival - buy one at any convenience store; it works on subway, buses and even taxis and saves queuing for single tickets
Tipping - it is not customary in Korea and can cause awkwardness; just pay the bill as stated
Booking a DMZ tour last minute - reputable tours sell out days ahead and require your passport details in advance
Only eating in Myeongdong - prices there are inflated; the same dishes cost 30-40 percent less in Mangwon or university districts
Transport without the tourist tax
From Incheon Airport take the AREX all-stop train to Seoul Station for about 3.50 EUR (roughly 60 minutes) or the Express for about 7 EUR. In the city the subway is fast and signposted in English - rides cost about 1.10 EUR with a T-money card, and taxis start around 3.50 EUR for short hops.