What's the best way to promote the opening of a new food establishment?
First though you need to identify your target market. Where are you? Who do you want to show up in your store? Besides children, what does your ideal customer look like?
These are some of the first questions you should begin asking before you ask, "How do I?" If you don't know your customers first, it won't matter how you start to market to them--you'd be shooting in the dark.
There are a number of ways to market your ice cream shop and I would start by getting the kids to hand out coupons of some sort. They're not hard to get, and they are cheap to print generally. Perhaps you can do a partial barter with a printing company in exchange for a discount on your ice cream, or give the executive team something to sink their teeth into.
You could also run a local ad in a smaller magazine or newspaper in your area. In which case, be sure it services your actual area.
You could always employ some guerrilla marketing tactics, too. For instance, you could have some kids take chalk and write your coupon on the curb for people to see as they walk by. Then if your customers mention they saw it on the corner of 5th and 13th, they get x percent off their next scoop of ice cream. Just make sure your employees aren't writing other things they shouldn't at the same time.
What is your brand? You are going to have to address that sometime. What makes your ice cream better than Baskin Robbins? or TCBY? They are well known, how do you intend to get known? What will your customers say about your brand? That will be up to you.