I stayed in Hotel Yonca for two weeks, which was clean and comfortable. Double Bed, TV and ensuite. There is a lovely lounge downstairs and a kitchen where you can cook. Free Turkish tea at your disposal. 24 hour reception. Some very helpful people working there although only expect two words of English, All for 25 YTL a night, which I think is about 13 euros. It is down the backstreets of Taksim where there are shifty looking people, but nobody gave me any bother walking alone at night. In my opinion Taksim is the best place to stay in Istanbul as you can reach everywhere very easily by the metro and bus station.
Hotel Yonca Toprak Lüle Sokak 5,(off Tarlabaşi Bulvari) Istanbul