- we are students
- we are sportive persons - any sport things
- budget is 100 euros
- historical things
- typical food
You can travel Hagia Sophia Istanbul Old City Blue MosqueIstanbul Archaeology Museums Chora Church Rumelihisarı Yıldız Palace and other Istanbul museums by buying a istanbul museum card, which is 85 TL or 26 Euros.
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this website would be able to answer a lot of your questions on festivals/Culture, food and historical monuments.
Since you are students travelling on a budget, have you checked www.couchsurfing.com ?