There really isn't any good ways that I'm aware of. (The exception is in New York or California, where hospitals must post prices.)
The law sets price floors on many procedures by setting Medicare and Medicaid reimbursement rates. As a result, the "list price" for a given procedure is dramatically inflated, and various health insurers negotiate rates somewhere in the middle.
I'd recommend talking to the business offices or financial counselors at medical groups that you do business with. Ask about "self pay discounts" or other programs appropriate for folks in your position.