Social media content shared today in cities, such as Instagram images, their tags and descriptions, is the key form of contemporary city life. It tells people where activities and locations that interest them are and it allows them to share their urban experiences and self-representations. Therefore, any analysis of urban structures and cultures needs to consider social media activity. In our paper, we introduce the novel concept of social media inequality. This concept allows us to quantitatively compare patterns in social media activities between parts of a city, a number of cities, or any other spatial areas. We define this concept using an analogy with the concept of economic inequality. Economic inequality indicates how some economic characteristics or material resources, such as income, wealth or consumption are distributed in a city, country or between countries. Accordingly, we can define social media inequality as the measure of the distribution of characteristics from social media content shared in a particular geographic area or between areas. An example of such characteristics is the number of photos shared by all users of a social network such as Instagram in a given city or city area, or the content of these photos. We propose that the standard inequality measures used in other disciplines, such as the Gini coefficient, can also be used to characterize social media inequality. To test our ideas, we use a dataset of 7,442,454 public geo-coded Instagram images shared in Manhattan during five months (March-July) in 2014, and also selected data for 287 Census tracts in Manhattan. We compare patterns in Instagram sharing for locals and for visitors for all tracts, and also for hours in a 24-hour cycle. We also look at relations between social media inequality and socio-economic inequality using selected indicators for Census tracts.