First off, there are four general types of escape games in Japan: 1) Room-type (single team trapped in a room/series of rooms) 2) Hall-type (multiple teams at separate tables in a conference room/hall) 3) Stadium-type (large areas like convention centers/stadiums, sometimes with no limit to team size) 4) Field-type (no team size limit and no time limit; play area ranges from in-store to city-wide)
In general, room-types are the best experience for beginners, since they are more immersive, you don't have the distraction of other teams, you're free to talk/make noise without fear of spoiling other teams, and you have the staff's full attention. I get the impression that the majority of games outside Japan are room-type, while hall-type and field-type are much more common in Japan.
If you just want to get the feel for what kind of puzzles you'll have to solve, field-types are low-investment, and are less stressful since you can solve them at your own pace.
Most of the games I would usually recommend for beginners aren't running, but out of the ones that are (that I've already played), I would suggest these if your Japanese is fine:
- 時空研究所からの脱出 (room-type)
- 下北沢謎解き街歩き (field-type)
- ある牢獄からの脱出1&2 (room-type; highly recommend going with a full group you know)
- マグノリア銀行からの脱出 (hall-type)
- のび太の宝島からの脱出 (hall-type; better if you like Doraemon)
These are also okay for beginners but may be better if it's not your first time:
- 2099年からの脱出 (room-type; this is a sequel of sorts to 時空研究所からの脱出)
- 不思議な晩餐会へようこそ (hall-type; the tables use projection mapping to advance the story)
- Escape from the Red Room (room-type; also can be played in English)
- The Mummy Escape Game (room-type)
- ある都市伝説からの脱出 (room-type; it's an escape game + haunted house, so only if you like horror)
- アイドルは100万回死ぬ2 (room-type; this one's a "time-loop game" where instead of solving puzzles you're trying to figure out how to successfully break the time loop, but very fun even for those who aren't good at puzzle-solving)
- Any of the Detective Conan games (hall-type)
- ドラキュラ城からの脱出 (hall-type)
- 監獄アルバトロスからの脱出 (room-type)
All of the suggestions above are SCRAP-produced games, since I feel they're entertaining even for beginners, especially if you're not sure whether you'll like escape games in the first place.
If you can't read/speak Japanese:
- Escape from the Red Room (mentioned above)
- Mystery Mail Box Global Edition (field-type)
- Tokyo Metro: The Underground Mysteries (field-type; the play area is city-wide, taking you to various Metro stations; not currently running but they've run one every year, generally starting in October)
- Any of the Escape Hunt Tokyo (recently rebranded as Nazobako)-produced games (room-type)