The very best ways to have access and information about art exhibits, galleries, places to show your work, and to be aware of all opportunities involving displaying and selling art is to join local and regional art groups in your area. They also have experienced artists, some of whom will share advice, as well as often provide educational programs for members.
I am an artist (have been for 23+ years) and the quickest way I have found to get established in an area is the local art groups. I have moved all over to various cities and states due to my husband's job and have had to establish myself many, many times. Some places were very small towns and there were still art groups and opportunities.
There are also online exhibits and competitions as well as statewide and national exhibits and competitions. Start locally and work your way up.