Academic occupation options for foreign visitors to the USA?
If you want to work or study in a program, you must change your visa type. You can file for an adjustment of status once you have found a job that will sponsor a different visa type or matriculate into a program that will also sponsor a visa for you. Tread carefully in your job hunting as job-hunting itself may be interpreted as a violation of your status -- it would be good for you to consult with an immigration attorney (or barring that, your university's foreign student's office) before you initiate this.

Otherwise, you are unable to work or study formally. The things that you can do:


Use your spousal ID card to study in the library
Use your spousal ID card to audit classes for non-credit
Enjoy hobbies -- join a maker club and make giant fighting robots, learn to fly a kite, etc.
Take part in the activities organized by your university's foreign student/scholar office (there are many spouses in your same situation, so they tend to offer things to help pass the time)
Cook, clean, take care of the children, and otherwise be a fantastic spouse to your wife