Yes, an RO system would be a very good way to go. They will get rid of the nitrates in your tap water, so the new salt mix will be nitrate free, and water changes will bring your tank nitrates down. RO also reduces any contaminants that might be in your water, and most come with a carbon cartridge that removes chloriene as well. An RO system is alot less trouble than a refugium.
A refugium is a seperate tank or compartment where macroalgae or xenia is grown to remove nitrates. There are hang-on-back and in-tank refugiums if you want to keep it simple, but for major nitrite removal, you're probably better off building a refugium into a sump system. The refugium needs a bright light, and a steady flow of water from the main aquarium. The macroalgaes and Xenia bind nutrients as they grow, then you can prune them back to completely remove those nutrients from the system.