Both would've been done by just changing translating the line in my case. We had Excel spreadsheets and one of the tabs was related to Menu and UI stuff. So in this case, they would just have to translate the japanese text at the bottom left to, say, "Shinjuku Station" (I don't know what it actually says) and that would be it. For the top-left thing, it depends how it's coded I guess. If it's text with modified fonts then that would still be easy. If it's indeed an artist that worked on that element and did one for every single day then yeah he would have to work on the localization.
I doubt that's how they did it though, seems like a lot of work when they could just code something simple enough that combines various elements. I suspect that's the case and they just select from a list what is tied to each day. For example, [Day of the Week], [Weather Icon] and [Time of Day], each of those UI elements tied to a font. For localization, they'd just have to translate all the lines that are in Japanese and copy-paste the text that's already in English (as a cell left empty would just read "LineID 100349"). So, say, Afternoon, Night, After School, Morning, etc. Then the game would display those lines in English when the language is set to English and in Japanese when it's set to Japanese. For example:
I don't know how they operate but in my case the artists wouldn't have had to work on anything in this scenario.
I'd personally assume that the time of day indicator in the upper left is probably art, not text stored as data. I believe (not 100% sure) Persona 3 and Persona 4 did it that way. Thus it probably requires being replaced for the English version.
Also Atlus has, in the past, replaced art within the game world. For example the sign for Hagakure in Persona 3 was altered for the English version. Paulownia Mall has altered art too, like the Japanese word for "Police" being replaced with an English one. So it depends on how much art like that would need to be modified.
Using PV3 as an example, seeing as the locations within this image can be entered, they might or might not have to alter them for the English version.