Omiyage is between the meaning of "gift" and "souvenir", omiyage isn't giving your friends and family something for a special occasion, and it's not something as casual as a 5$ souvenir it's a little bit more than that. Just know that whenever you visit somewhere you are obligated to bring something back for those in your social circle.
For Those of You Homestaying
If you plan on staying with a Japanese family for the next couple months the first thing you should do is buy omiyage. The best thing to bring is something from your home country like food or something unique that your city makes. If your hometown isn't really known for anything just bring something that represents your hometown like a t-shirt or mini-statue. If you plan on bringing food as your gift buy it from the store, don't make anything homemade. Bringing something special to your host family will give them a great first impression, and will break the ice.
What Should I Bring Back if I'm Already in Japan?
When visiting different prefectures try to research what that prefecture is known for and bring that back, for example: Tochigi is known for Reito Nama Gyoza and Aomori is known for their Ki ni Naru Ringo. If your in a rush and have a hard time finding anything sweets are usually the best default. Because omiyage is engrained into Japanese society there are plenty of tourists shops that offer neat prepackaged omiyage filled with chocolates and other sweets.
Don't hastily wrap your gift, it shows that you don't care. Usually, if you're buying omiyage in Japan they will come prepackaged for you, but if you're coming from your home country or buying something else in Japan have someone wrap it for you.
When in Doubt Break the Snacks Out!
Try to keep in mind that space in Japanese homes are limited, so try not to bring back something that will take up space. When buying omiyage it's best to bring back food, remember if you're going to a prefecture known for a specific food bring that back. You can buy little trinkets like a small statue, but try not to burden the receiver by trying to find space to put your gift.
I guess the main point of this article is just bring back good food for people, and make sure it looks good. I hope this helped you on preparing to visit Japan so you're not caught off guard by people expecting gifts from you, this was something that didn't really occur to me so I figured I would spread my wisdom!