Help Me Find a JRPG!

take a look to "the last remnant". A really really hidden gem. Very underrated. It has a name for the "subgenr" but i can't remember. Basically its anti grinding. There are random encounters but you can see the monsters, so you can avoid them... for your own good, its a system that can backfire at you. There are no levels per se, so the monsters upgrade his stats with you, making practically impossible to beat the game if you fight a lot :)

You're describing Celestian Tales quite well.
No random encounters, you can see where all enemies are (you can't see what's inside every encounter, but you can at least see them coming)
Game sadly does not let you save whenever you want, but save points are frequent.
Health and status ailments resets after each battle. The only exception being if a character falls during a battle, at which point it will get a "wounded" status.
No over-sexualized characters. While the topic of sex is mentioned, none of the characters are sexualized.
No crafting (thus far)

You might also want to check out Tales of Symphonia when it gets released on steam. It once again won't let you save anywhere (unless they add that to the PC version), but you won't have to worry about random encounters, the characters are not over-sexualized (in fact there is very little direct mention of anything of that nature, and only one character has some questionable poses (and it's not that bad). Health does not reset between encounters, but the game is quite forgiving. Very light crafting.

I think Septerra Core matches your requirements. I find combat to be a bit repetitive though but the game is brilliant.

The dark cloud series. Especially the second one.
Every other JRPG is irrelevant xD
These games are emulatable, if you don't have the funds to buy them and the ps2 as well.
The game focuses on Town/Weapon crafting, however these games are extremely casual.
The second also deals with time so town wise when you craft you'll get to see what it changes in the future.
Also has the best original soundtrack when it comes to JRPG's.
Plus all the levels are random so it's highly replayable.

Tactics Ogre

Any preference for platform? I'd suggest Mother 2, my favourite in the genre.

That's probably very obvious but... Final Fantasy 12 ?
Rogue Galaxy (PS2)
Tales of Symphonia (obviously ^^) Game cube/wii
Tales of graces F (PS3)
Baten Kaitos (Game cube) Best RPG ever :)
Sky of Arcadia (Gamecube too)
Eternal Sonata (a little bit harder if I refer to your criteria)
I Will think of other ones ^^

I'm here to contribute one piece of information : You're asking for a JRPG that isn't a JRPG which is a pretty tough description to fill. EIther you go for the suggestions in this thread (Which are the best you'll get) or you go for a WesternRPG, e.g. Baldur's Gate or such. Personally, I think Chrono Cross is a good choice. It's pretty simplistic, its music is amazing and its story is captivating.

EDIT: Also, something that rings in my heart as an amazing playlist of JRPG/RPG(I say RPG in general because not sure if they're all JRPGs) songs from games. If you want to listen to music and get an amazing list of games that are regarded as being classics (Wild Arms, for example! Still have to actually play the first one, or any of them for that matter) then go wild! MUSIC

I've been wanting to get into JRPGs for a while now too so threads like these are always fun. Seems like it depends on the time that it's posted, though. This site gets pretty dead in the chatting area at later times.

The Last Remnant?

Penny Arcade's On the Rain-Slick Precipice of Darkness 3 is pretty fun, gives the illusion of random encounters, but they are specifically set up. It's turn based, plays kinda like FF6. The game is full of JRPG style plot, music, and visual style.