Saint Augustine is easily navigable by car. The downtown area can be congested, especially as of the date of this publication (October 2009) while the Bridge of Lions is undergoing construction. There are a few major roads that can bring tourists through the town. US1 runs north to south and passes right past the downtown area. A1A runs next to the beach. Many beach-side hotels will have an A1A address. The majority of this road is two lanes.
It is difficult to stay in Saint Augustine without a car, but it is possible. Public transportation is severely lacking, though private taxi's are always available. If you do not have a car, stay on the beach or in the downtown area in one of the bed and breakfasts.