Chrono Trigger.
Shit, this. It's fun, it's straightforward, it's got excellent visuals in and out of combat, and it's got a great soundtrack. I know someone who didn't like RPGs at all and played Chrono Trigger top to bottom pretty much without putting it down.
I'd also recommend the Golden Sun games. I really enjoyed them, plus they have a lot more focus on advancing through the game then they do on grinding.
Earthbound is also a really good game. I haven't tried Mother 3, but Earthbound is an amazing game and really tailored for people who don't like grinding. It has touch battles, and you don't even have to fight weak enemies! Plus, it doesn't take itself seriously.
My first RPG was Final Fantasy Mystic Quest. I had the map up on my wall and everything. After that, everything just seemed better and better!