The key here is HOW you are going to generate your leads, whether they are phone numbers for SMS marketing or email addresses for email marketing...
You can't just text message or email everyone in a specific area of a city without having their information and permission first so you must set up a campaign to generate leads first...
Do you have the knowledge / tools to set up a proper SMS marketing campaign?
It would also help to know the demographics of the target audience... If they are younger, older, etc.
Instead of it being "AdWords vs. SMS or Email Marketing" ... You could use AdWords to drive traffic to a squeeze page where you collect your leads' email addresses or mobile numbers. They can all work together. Does that make sense?
Best,
Shane