I wouldnft exactly call Odaiba/Ariake/Toyosu a local place, but if you like recreational train riding, the Yurikamome Line is just plain fun. Day passes are a little expensive, but if you sort of make a day of it and get off and on several times one will pay off. I just have great memories of riding the train itself. I guess you could also ride a boat (water taxi) and/or walk across the rainbow bridge. (I havenft done either but it might be fun.) If you havenft been to the new fish market it might be worth a visit just to see what it is like now. (Tourists who were passionate about Tsukiji tend to pan it because it is nothing like Tsukiji, but Tsukiji had gotten to be just dreadful because of all the tourists.) I havenft been to it yet but if I had lots of days to burn in Tokyo, I would definitely make one day a Yurikamome day, ride the train to my heartfs content, and make several stops along the way, possibly including one to just check out the new market. I know that at least one of the shopping venues (Venus Fort) has closed (I never really cared for it anyway) and the ferris wheel that was out there has ceased operation, but there are other things to do. Just walking around Odaiba for the views is enjoyable.
If you havenft been to Shibuya for a while, there are a number of new venues there. I never cared too much for Shibuya myself, but the new complexes there look quite attractive. (Japan Guide has some writeups.) Of course, Shibuya is the opposite of a local place and maybe what you are wanting to avoid.
I always like Meiji Jingu early in the morning. It opens at dawn, with no closure days. Again, it is a not exactly a glocal place,h but the atmosphere early in the day is terrific, there are very few people there. I enjoy walking through the shrine and ending up in Shinjuku, finding a good bakery, and heading back to wherever my hotel is to eat some delicious breads for breakfast in my room. (If it is rush hour itfs a terrible time to ride commuter trains, but I have found workarounds that arenft too bad.) If you get to Shinjuku after 9 a.m. you can visit Shinjuku Gyoen, which isnft a glocal place,h either, but since they charge admission it tends to keep the riff-raff out. It has never been crowded the few times I have gone, and I enjoyed the greenhouse. (It has different hours than the garden at large, as I recall.)
Of course you might already be aware of all of these things. But one thing about Tokyo is that it is dynamic and constantly changing, and even the hstandardh places can be worth revisiting every once in a while.
Over the years I have gotten a lot of great ideas from Time Out Tokyo:
https://www.timeout.com/tokyo