In the game, there are suggested sites for settlement with the golden icon, but is there a way to see which titles are valid or invalid for establishing a new city? The restriction of neighboring cities is not always clear.
From the wiki:
Cities have to be at least 4 tiles apart of each other. That includes your cities, as well as other civilizations' cities, and it prevents littering the map with cities. Other than that, cities may be found on any tile where a Settler unit may move to (including a 1-tile island).
Basically, using this rule manually gives you a general idea of where to settle in proximity to other cities, but there is no interface built into the game that I am aware of to warn you of your city's proximity to different city's, other than having a settler at the spot you wish to settle. This information should be enough though for your purposes.
More information can be found here: http://civilization.wikia.com/wiki/Settling_a_city_%28Civ5%29
In addition to Rick_Roll's answer, You may accomplish this via
For example, I currently use this mod that does the exact thing you want: Civ5 - City Limits
It highlights tiles that are invalid for settlement when a city or settler is selected.