Yes, you do need a website, although if you want you can use your blog as a website. There are some differences between the two though.
Most specifically, a website offers more customization. You can get the exact images, colors and layout that you want when you work with a professional website designer to get it exactly the way you want it. It is sometimes – but not always – a little harder to have ongoing updates to a website, it is very easy to do that on a blog.
I usually recommend a basic website of 5-10 pages. If you plan to focus most of your efforts on SEO, then you will need to have at least 25 individual keyworded pages on your site. This is often easier to do on a blog. If needed have one or two of those pages set to be easy to update – for instance if you are a restaurant you might want to make frequent menu changes. If you work that site right, and get your keywords straight right out of the gate you should be on the right track.
Then add a blog to your website, that will give you more flexibility to talk with your customers. This will look nice and very professional, and it really does not have to be expensive.
Brick and Mortar stores have a wonderful chance to get google traffic to their website, even without SEO. Google makes efforts to give the surfers the best experience. If you go to your google and type in your city name + the main topic of your store – for instance: Glen Ellen, CA + Chocolate, then you get all the stores that specialize in chocolate around that city. They come up with a google map and the links on the right side. Some of those listings will have a url that starts with maps.google.com. This means that the business is on the coveted first page without paying for it, yet they are not taking advantage of the position. This is about the saddest negligence of a huge opportunity that I know.