Galata Tower (Tower of Christ, called by the Genoese), once city's tallest structure when it was built in 1348, Istanbul's "most striking landmarks", happened to be close to Galata Flats (Tunel-Beyoglu area) where we were staying last year (2012). Naturally, we ventured to cover this landmark first, knowing well that it also have good eating places. However, the area is hilly with narrow sidewalks, at times difficult for pushing stroller with a baby.
There is a restaurant and café on Galata Tower's upper floors plus a night club, none of which we tried as we had lots of small children with us and were more interested to capture the views of the Old Istanbul, as long as there is good light.