You're limiting yourself, but the next logical steps would be Final Fantasy V Advance and Final Fantasy VI Advance.
Final Fantasy VI is much more critically acclaimed, and is an amazing game. I also thoroughly enjoy Final Fantasy V, so you really can't go wrong with either. (Especially the GBA localization of FFV, so good.)
Final Fantasy I is also a lot of fun, but I wouldn't recommend playing the watered down "Dawn of Souls" version available on the GBA. I know it's not on a Nintendo system, but if you can get ahold of it, the Final Fantasy Origins edition really is the definitive version of Final Fantasy I. I'd actually rather play the original NES version than the Dawn of Souls version, but that's probably just blind nostalgia (read: I do not like the Dawn of Souls version).
Final Fantasy II (Also available in the Dawn of Souls collection and not nearly as neutered) is good, but probably the last one I'd recommend of the NES/SNES generation. It has a radically different leveling system, that's novel, but usually just winds up being abused.
I love Final Fantasy Tactics (PSX/PSP), but I don't particularly share that love with the Final Fantasy Tactics Advance spin offs. But if you'd really like to play one, or just want to play a SRPG/TRPG, I enjoyed FFTA2 more than the first.