A good place to start is HealthCare.gov. This is the health insurance exchange created by the The Patient Protection and Affordable Care Act, and is a one-stop shop for private individual market health insurance plans (note that the exchange itself is run by the government, but the health plans for sale in the exchange are all private, from the health insurance companies with which you're already familiar). People in 39 states use HealthCare.gov to enroll in individual market plans. The other 11 states and the District of Columbia have state-run exchanges, and you'll be directed to their sites from HealthCare.gov when you select your state.
There are other online brokerages, both large and small, that can help you sort out the individual market health insurance options available in your area. Most of them can show you plans that are available in the exchange as well as options that are only available outside the exchange (no subsidies are available outside the exchange, but as noted above, you're probably not eligible for subsidies anyway, if you have access to an employer-sponsored plan).