Dynamic social media content, such as Twitter messages, can be used to examine individuals' beliefs and perceptions. By analyzing Twitter messages, this study examines how Twitter users exchanged and recognized toponyms (city names) for different cities in the United States. The frequency and variety of city names found in their online conversations were used to identify the unique spatiotemporal patterns of "geographical awareness" for Twitter users. A new analytic method, Knowledge Discovery in Cyberspace for Geographical Awareness (KDCGA), is introduced to help identify the dynamic spatiotemporal patterns of geographic awareness among social media conversations. Twitter data were collected across 50 U.S. cities. Thousands of city names around the world were extracted from a large volume of Twitter messages (over 5 million tweets) by using the Twitter Application Programming Interface (APIs) and Python language computer programs. The percentages of distant city names (cities located in distant states or other countries far away from the locations of Twitter users) were used to estimate the level of global geographical awareness for Twitter users in each U.S. city. A Global awareness index (GAI) was developed to quantify the level of geographical awareness of Twitter users from within the same city. Our findings are that: (1) the level of geographical awareness varies depending on when and where Twitter messages are posted, yet Twitter users from big cities are more aware of the names of international cities or distant US cities than users from mid-size cities; (2) Twitter users have an increased awareness of other city names far away from their home city during holiday seasons; and (3) Twitter users are more aware of nearby city names than distant city names, and more aware of big city names rather than small city names.