Do you have budget? For the best chance at catching a blue, the FAD trips out of Costa Rica are probably your best bet. They require running over 100 miles off the coast and an overnight on the boat.
Otherwise the DR has a good blue Marlin bite.
If you are wanting to stay in the US it's hard to beat Oregon Inlet, NC for white Marlin, and an opportunity to catch a blue. They have the what is arguably the best charter fleet in the country between the Oregon Inlet fishing center and Pirates Cove Marina.
Other good international destinations are Cabo San Lucas for striped Marlin, Tropic Star Lodge in Panama for Blacks, Australia for Blacks.
Kona, Hawaii is also a good place for Blue Marlin.