If you decide to buy gold as an investment, then I'll assume you are spending over $10,000. If you are talking a single ounce or two then it's a different story. Through a broker you can buy a large amount and not actually take possession of any gold. You will be basically "playing the market" and the broker watches the price shifts and advises you when to sell or hold or even buy more as you build up interest.
Many people are not comfortable with "paper gold" and want to be able to actually hold their precious metal (like me). In that case, there are gold dealers you can find online. If you check kitco.com you will not only be able to track gold's value, but there are brokers on the site that are reputable. If you are just buying small amounts of gold then your best place to buy locally is a coin shop. They sell gold with the price changing along with the market. They sell gold at the spot price plus 3-5%. That's how they make some money, just like a broker does. Spot price is the exact amount that old is selling for on the world market at any given moment. Once again I'll suggest going to kitco.com to see the spot price. That price is changing based on the value of the US Dollar in the world and by how much gold is being purchased anywhere
So buy gold at the local coin dealer. Second best is jewelry stores, but be prepared by knowing the spot price and that it should not be marked up by much more than 5%. Stay away from pawn shops. They are more concerned in making money than you getting a fair deal and they will jack the price up way over what it should be. GO look at some of my other answers to people about gold inesting, particularly the one titled, "Poor Girl Wants To Invest In Gold". It answers some more of the things to know about gold investment.
By the way. I am in no way connected to kitco.com. I use them as a reference simply because I have always used their site to watch gold prices. There are many other sites similar to this one, so look around.