If you want a big city EMS system, look at FDNY EMS, Boston EMS, Newark EMS, Jersey City EMS, Philly FD/EMS, DC FD/EMS, Pittsburg EMS, Seattle Medic1 or just look up the largest cities you would be open to moving to, and look up their EMS provider.
As was mentioned, most biggest systems have higher turnover rates, and most hire every 3 to 6 months, so you fill out the application, and they will contact you when they are doing the evaluation process.
Wake County EMS, Durham County EMS, and Orange County EMS are all county EMS systems with at least one big city in their coverage area. Yes, Skip runs DCoEMS, and he is a friend of mine, but I have paramedic and EMT friends at DCoEMS who are unhappy there and looking to get out. Skip definitely has his work cut out for him, and he has been lciuooking to add good people to the system and get rid of people that need to be gotten rid of. And Durham Co pays relatively poorly, but they do give you a higher rate if you have experience at your level in EMS.
Even the guys at Wake will tell you it isn't a utopia, despite what their PR guy says, and Orange County is making constant improvements. MEDIC in Charlotte is a great place to gain experience, but I hear they run their crews into the ground, and have a high turnover rate (although Wake is almost as bad), although that is typically higher with most urban systems.
If your youngish, single, and have some money to burn, send applications to everywhere you want to work (and if you get into Medic1 in Seattle, consider it awesome), and finish their assessment centers, and see who offers you a job. You can do your own research for large cities, and if you have questions about particular systems, feel free to ask if anyone has experience with them.
