You might want to look into Akiba's Trip, and eventually Akiba's Beat once its release. Akiba's Trip takes place exclusively in the Akihabara (Akibagahara) district. If I remember correctly, they painstakingly worked to make the game look as close to the actual area as possible. They even left the Japanese advertising for real-life Japanese locations.
That's one I was actually thinking about. The game is real goofy, but I heard they did a good job recreating a section of Akihabara. That's one I can actually pick up pretty easily being on PS4. I went to the flea market today and checked a couple vendors, but no luck on Persona or Yakuza.
I can't speak for the console version, but the Vita version is kinda icky. The controls need work (you can move the thumbstick a pretty decent ways without getting any rotation in game). I didn't play it for long, though.
As for Akihabara (since someone mentioned wanting to visit Japan), go during the night, not the day. It's a lot cooler at that time. I was actually pretty disappointed, though, because I thought it was a pretty large area, but it's only a few blocks (and really, mainly one road).
P3 is on the PSP, and P4 is on the Vita (if you're looking for alternative versions). My emulator is a bit slow for the PSP version on my PC. Do keep in mind that the PSP version does lack some visual elements the original had, but it's still a very good version (I nearly finished a review, but never got around to doing the final check and edits, unfortunately).
As for P3 vs. P4, everyone has their favorite. P4 makes some nice gameplay improvements, but I still like the visuals and darker story of P3. That being said, one problem (unless you play the PsP version) is that you don't have AI control over your party members. And P3 can already be frustrating enough at times during boss battles, so that alone makes me want to recommend that version instead of the normal PS2 version.
Atlus does have sales on the PS Store from time to time, so if you follow the facebook page, they'll post when there are sales.
You could try Persona 2 as well (PSone classic or emulate). I just find it hard to play anything older than P3, because it feels a bit clunky going through all the battle menus. I would wholeheartedly recommend the OSTs of any game, however.
Also, FYI, Persona is a sub-series of the Shin/ Megami Tensei series. The other games are also RPGs, but (basically) lack the social life simulator mechanics, in favor of different ones. So you can check out any of those games, especially if you like mythological/religious figures, as the 'demons' in the game are icons from different cultures/religions/myths/etc. I enjoy reading about them.