The trademark symbol informs anyone who sees it in conjunction with your logo that you, as the logo's owner, are asserting a right over a specific graphic. It defeats the purpose of displaying the symbol if you confuse the public about what you are claiming as your trademark. If you place the symbol within the graphic or where it cannot be distinguished easily from part of the design, you make it more difficult to protect your trademark.
The USPTO does not mandate a specific location for the trademark symbol. The most common location for the symbol is to the right of the logo, at the top or bottom, according to the International Trademark Association. The symbol should be immediately adjacent to the logo, regardless of which side you place the symbol. If you place the symbol where most people expect to find it, you increase the chances that the public and competitors will understand your intent to assert your claim to the logo.
If you are asserting a claim in a logo, whether you have started the application process to register your trademark or not, the USPTO regulations permit you to use the TM or SM symbol for trademark and service mark, respectively. You may only display the symbol of a registered trademark, an R within a circle, if you have duly registered your trademark with the USPTO. If your application is pending and not finalized, federal regulations do not allow you to display the registered trademark symbol.
Choosing to place a symbol next to your logo does not mean that you will prevail in a trademark dispute. Many other factors are involved in the successful prosecution of a trademark case. Placing the symbols may help to prevent other parties from using your design. If no one else uses your logo, you reap all the benefits of your trademark and avoid all of the ill effects of infringement without having to bring a lawsuit.