In my opinion, Quantitative research using hypothesis testing will be the best, as per your objective (urban adolescents) you can frame a set of questions and perform a survey on heterogeneous population (offline and/or online) will be the best method.

You might be interested in the California Healthy Kids Survey http://chks.wested.org/administer/core#core

If this is a cross sectional survey, commonly used descriptive tools, when census or non-probability sampling was involved, are measures of central tendency, measures of spread and measures of association (depending of the the type of measure of the variable being studied). If probability sampling was used, inferential tools like tests of significance of difference, tests of significance of relationship, and one-sample T-test or Z test would more likely be needed.

I am agree with Eddle Seva See

One can also think for association mining, clustering, classification and prediction from survey.

You're on the right track. I'd suggest use of questinnaire, indepth interview and focus group discussion among a sample of the adolescemt population after all ethical issues have been duly considered and addressed.

I just finished a study on Nigerian adolescent and youth immigrants in Minnesota. I found that it was relatively easy to conduct a quantitative study with the group given that the validity and reliability of the instrument have been tested and considered appropriate. Giving that my sample included adolescents, age 12-17, and youths, age 18-24, I needed two different consent. Adolescent could not consent, therefore, their parents/guardians had to consent for them. One of the feedback I received was that if it was an interview or focus group, I would have needed the consenting parties to sit in on the interviews or focus group. So if you could get the consent that you need, a qualitative method would in fact yield a much more in-depth result.

If You want to assess the behavioral problems among the adolescents it's better you can go for child behavior checklist, its a standardized tool to assess & most convenient tool as per me.