The urban forest contributes to the improvement of the air quality, through the removal of its pollutants and carbon dioxide absorption, mitigation of noise pollution, improvement of the temperature, water quality and hydrological cycle, urban ground and benefits such as real estate valuation and stress reduction. For more details please have a look at the following RG links.
Article Urban Forests and Their Ecosystem Services in Relation to Human Health
Article Urban forest benefits to the younger population: The case st...
Article Understanding the benefits and costs of urban forest ecosystems
Article Assessing the Benefits and Costs of the Urban Forest
Chapter Understanding the Benefits and Costs of Urban Forest Ecosystems
Chapter Urban Forests and Human Well-Being
Chapter Urban Forestry for Multifunctional Urban Land Use
Article The benefits of urban and peri-urban forestry
Conference Paper Ecological Benefits of Urban Trees
Conference Paper Urban Forestry in Africa - Insights from a Literature Review...
Technical Report Delivery of ecosystem services by urban forests
From the environmental perspective, you may wish to check various reports of the Intergovernmental Panel on Climate Change which focuses on urban forests. Such include: IPCC Fifth Assessment Report The Role of Forests
Concerning urban forest management, you may like to check this report as well: Climate Change Mitigation and Adaptation in Urban Forests: A Framework for Sustainable Urban Forest Management http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.388.4681&rep=rep1&type=pdf
Also, A framework for adapting urban forests to climate change - https://www.fs.fed.us/nrs/pubs/jrnl/2016/nrs_2016_Brandt_001.pdf
This is a very interesting question. An irony to notice that the few forest in urban areas (meant to improve the air quality among others) keeps being pulled down and developed into residential and commercial centers.
This other link is from a very interesting project called "Treepedia". This is the Green Viewing Index (GVI) estimate, based on Google Maps imagery, the index represents the perception of tree cover in large cities based on trees that people see when walking. The site also provides a wealth of information on the benefits of trees in cities: http://senseable.mit.edu/treepedia