In a life-threatening emergency, call 911 to summon an ambulance to take you to the nearest hospital emergency room ("ER"), or in less urgent situations get to the hospital yourself and register at the ER's front desk. Emergency rooms will treat patients without regard to their ability to pay, but you will still be presented with a bill for all care. Do not use ERs for non-emergency walk-in care. Not only can this be 3-4 times more expensive than other options, but you will often wait many hours before being treated, as the staff will give priority to patients with urgent needs. In most areas, the charge for an emergency room visit starts around $500, in addition to any specific services or medications you may require.
Walk-in clinics are the most convenient place for travelers to find routine medical care, letting patients see a doctor or nurse-practitioner without an appointment (but often with a bit of a wait). They are typically very up-front about fees, and always accept credit cards. To find one, check the yellow pages under "Clinics", or call a major hospital and ask. Make sure to tell the clerk you will be paying "out of pocket"; if they assume an insurance company will be paying for it, they may order tests that are not medically essential and in some cases bill for services that aren't actually provided.
Dentists are readily available throughout the United States (again, see the yellow pages). As most Americans do not have dental insurance, dental offices are accustomed to explaining fees over the phone, and most will accept credit cards.
Most counties and cities have a government-supported clinic offering free or low-cost testing and treatment for sexually transmitted diseases; call the Health Department for the county you are in for more details. Many county clinics offer primary health care services as well, however these services are geared towards low-income residents and not foreign travelers. Planned Parenthood (1-800-230-7526) is a private agency with clinics and centers around the country providing birth control and other reproductive health services for both females and males.