Are there locations on Earth that only have one season?
Due to the obliquity of the Earth, no place would truly have a single season, which in this answer is taken as having consistent conditions, particularly in terms of temperature and precipitation.

An environment that would qualify as having minimal seasonality are in the equatorial tropics, which according to the article Climatic seasonality, resource bottlenecks,
and abundance of rainforest birds:
implications for global climate change (Williams and Middleton, 2008) due to the almost consistent insolation, as shown below:

 

Image source - the blue line represents the yearly trends across the year for  equatorial regions. 

Although, according to the article, the temperature remains fairly constant, precipitation can have alternating wet and dry periods, and can affected by other climatic factors (depending on location) such as El Niño, monsoons etc.

However, according to the Köppen climate classification system, the closest environment that would have minimal seasonality is classified as Af, which are warm moist rainforest, located in the areas shown below:



Image source

An example of a location in such an environment is the city of Andagoya, Colombia, South America, (latitude 5N, elevation 65m) which has the following annual temperature and precipitation:



Image source: Climate Classification and Climatic Regions of the World, which describes the classification Af as lying within the influence of the Intertropical Convergence Zone (ITCZ) and experiencing very little variation in temperature and precipitation throughout the year.