What are some of the most innovative, impactful ways to build awareness for a new retail location? The leaner the better.

Grass roots marketing is always best (and cheapest). If you are near schools, "partner" with the schools and offer incentives for the school - for example, 15% of sales this Tuesday will go to John Smith Elementary, just come in and tell us you are with JSE. Get the school's buy-in and they will promote it for you. Provide them with stickers to give the kids that remind their parents.

Another great proven way is to employ college kids to promote your business in exchange for free food.

Also, Fiverr.com has a lot of VERY inexpensive options for local marketing.

Depends on your industry. I love what Red Robin did when they came to my town. They sent out packets to a select group of the community and invited them for a free lunch in the two weeks prior to opening. Guests received a controlled, informative, free lunch for four and the company received a 2 week training event for a whole group of new staff. Even though I don't eat their often, I have such a positive view of the company based on what they did and recommend them to others.

Hope that helps!

Retail is close to my heart. I have been working with retail corners and try to understand each retail sector across the state.
First thing to understand is where you are looking to position yourself ?
What is the market you want to target? What audiences you going to prefer? And how to give them an over an edge experience with they getting service/product from you ?
People in retail are creating customers, I prefer to create fans and audiences for the brand's which helps them in a long journey.
Customer buys product once whereas fans are the people who will promote your retail brand to others and will always look forward to you.