Hello Rob,
In order to improve your local SEO you would need to claim (or create) your company's 'local listing' pages across platforms. A lot of websites out there list local businesses such as Google Places/Local, Yahoo local, Foursquare, Hotfrog, Yelp and much more.
Many of these platforms allow you to claim the page where they give out your company details so you can fill in the information about your company yourself. Once you've done this you need to make sure the information there is correct.
Enter your company name, address and contact details everywhere in the same way. For a computer it's very difficult to understand that avenue is the same as 'ave' in an address.
Fill in a good description, add photo's/video's if you have any and make sure the listing describes clearly what your company does and what it is all about.
The most important one of these is your listing on Google Places/Local. This page will actually rank in the search results as you described. Make sure you fill this in as good as you can. Google will use this information and compare it to other listings of your company. If they see that the information is consistant this would indicate to Google that the information is correct and they will trust you more and more. This would help you rank better in local SEO for related search queries.
Another good thing to remember is that reviews help you rank too. If you've got loyal and satisfied customers, ask them to write a review for you on your Google Places/Local page.
Note: Don't pay people for reviews or anything. It's against google's guidelines to buy or sell reviews just like links.
Some resources to get you started:
Hope i answered your question. If anything was unclear or if you have any more questions please let me know and i will do my best to answer or explain more.