This is just an addition to kennansoft's solution:
Important
Probably the most important destination is China Town. Every other location either can't be missed or is much easier to get. China town can only be unlocked from the booj Chinese Sweets, which is an end reward for the request "Part-time job, full-time hell". This request is missable! Make sure to level up your Moon Confidant to rank 4, and read every text you get from him so that you don't miss it.
Save Time
You'll kill 3 birds with one stone by doing these actions first. Once you've reaped the benefits of the event and also unlocked these locations, you can "read" the book, at which point you'll get the book marked off, but no time will pass.
-Destinyland is unlocked as part of the story.
-Inokashira Park is unlocked at Lovers confidant rank 3
-Ogikubo is unlocked at Chariot rank 4 (theoretically missable if you avoid ranking up Chariot since there is no book)
-Jinbocho Book Store is unlocked at Star rank 4
-Ueno unlocked at Emperor rank 3 (also no book and potentially missable)
-Asakusa unlocked at either Lovers 7 ot Star 6
-Tsukishima unlocked at Chariot rank 7 (also no book, potentially missable)
-Odaiba Seaside Park unlocked at Lovers rank 10
Optional Opportunities
Be sure to check your texts on a day off, because you could get invited to a new place, and many of these events end up earning points to your confidant level for the person who invited you, and usually one other person that you bump into along with unlocking a location. This is more of a judgment call based on your confidant standings.
-Fishing Pond invite on 7/2 by Chariot (+Temperance points?)
-Planetarium invite on 7/28 by Moon (+Emperor points)
-Harajuku invite on 8/3 by Moon (+Chariot points)
-Meiji Shrine invite on 8/5 by Lovers (+Death points)