If it's games, I highly recommend some older fantasy titles like Final Fantasy (my favorites being IV and V; IV is a lot more story driven than V though). I definitely would not, 100%, start with something like (Shin) Megami Tensei games; the language in them is much more difficult (from the ones I've tried playing in Japanese) than most typical medieval fantasy games.
If emulating older games scratches at your moral fiber too much, then go for a handheld title, like some others have mentioned; they're usually easier to find, and you can get rereleased versions of older games on them. Also, there are far fewer auto-playing events in handhelds (though that's changing recently). If you like the Pokemon series, the last couple generations offer two versions of their scripts, one all kana, one with kanji (still not very much, but it _is_ for kids...).
Spirit Tracks offers a really useful 'tap for furigana' feature... too bad the game isn't a bit better (I'm really wanting a remake of the GBC Zelda games with the planned third one added in, but that's beside the point).
And Golden Sun is a superior RPG experience; the third game isn't as good as the first two by a long shot, but it's still fun. I haven't looked at the Japanese versions, but it doesn't seem like it'd be confusing in Japanese for any reason other than a slight lack in dialogue.
And I didn't find Tales of Phantasia too difficult in Japanese (I played the GBA version, but apparently there's a PS2 version with voiced story scenes); it's a fun change from the 'mash the A (or O) button over and over' gameplay. The story is good too.
I've been really into the Summon Night games recently (only played the first and fourth main games, and the GBA spinoffs so far); all that I've played has been wonderful fun. Probably not the best game series to start with, since there are choices that determine how certain things will go (the MC and their stats (simple questions), whether you'll encounter or recruit other characters, and other things that I haven't quite figured out yet); I can't say that all of these choices are particularly important to what happens overall, but choices I can't understand make games less fun for me (took me forever to actually play the first one after I got it, because I couldn't make one of the first choices after the story starts). Most of them have been re-released on the PSP (excluding the newest ones, of course), so it's really easy to get them.
As for some PS2 games: the Kingdom Hearts games (the properly numbered ones, CoM wasn't as tolerable on PS2 as it was on GBA) are really fun, but they make use of cutscenes quite a bit, so if that's too fast, then they probably won't be quite so fun. (Personal note: it's weird as hell hearing Disney characters speak in Japanese, and the same for most everyone else in English; there's no winning, so it might just be more enjoyable to pick the ones that sound least weird to you instead).
And, um, there's also the Ar Tonelico games... Not much of a common taste, these games (and even I'll say that the PS3 one sucks), but if you can like them, they're actually pretty fun games, but, um, maybe don't play them with anyone else around... And wear headphones... I might be exaggerating, but they're a couple of the games that I just don't tell people in real life that I've played.
Anyway, all of the dialogue is in text boxes (IIRC, most, if not), and events are handled with VN style text boxes. The combat system is rhythm based on the defensive, and based on simple button inputs on the offensive, which is actually quite fun most of the time.
It's been a while since I played these last (before I knew much Japanese, though I did undub them...), so I can't remember a lot of specifics about how easy they would be to read (not that I've played them in Japanese yet), nor how much was voiced.
And for a quick not-RPG, the Professor Layton games are pretty fun, and though the puzzles don't always require instruction to solve, it can be a decent exercise in understand instructions and solving puzzles (duh) in Japanese.
Ultimately, VNs (for PC) and web novels are a lot easier to get into, as far as looking things up, but sometimes you want to play games, and you might as well play them in Japanese if you're feeling up to it.
Edited: 2016-06-03, 11:27 pm