Other than dinner reservations and maybe a couple of lunches, this is exactly what we intend to do. My Tokyo itinerary is basically a list of neighborhoods starting with those closest to our hotel and filled with all points of interest (not necessarily tourist attractions or major sites but many local things that would never find their way to this forum) and our plan is to just spend each day walking until our feet hurt, exploring as much of the city as we can!

As for chosing restaurants at random, I've selected a couple of low-key spots to mix with locals and enjoy casual meals (such as Ishii) and that's what we'll be doing for most lunches. We have some room to explore and discover during the day, but there's honestly so many places that I want to try and so little time that I've opted to do as you've suggested for other cities instead. We're basically spending a week in Nagasaki doing just that. We really only have 7 days in Tokyo, so while I'm sure wandering into random places for chance meals could be really rewarding on many levels, we plan to return in a year or two and spend more time doing just that. We'd probably get an apartment through AirBnB for a couple of weeks and do exactly as you suggested. With only 7 days for our honeymoon, I'd prefer to seek out as many of the places that I've read about and anticipated visiting for the past 2 years as possible. We have plenty of time to spend drifting through depachikas as Robyn suggested, tsukemono shops, etc. I've not planned out anything for our days beyond highlighting a few *must visit* places, the rest will just be left to chance and circumstance. I've only really planned intricately for the small towns that we're visiting for 1-2 days at most, since they're destinations that we're seeking out for specific sights and have limited time and more focused plans as a result. I agree with your advice though!