For outings from major German cities like yours, Earl Steinbicker has the very best day trip ideas in print, IMHO.
It's a common misconception that a "hub and spoke" plan must use big-city, post-WW II-construction hubs like the ones you are considering. Germany's rail network is dense, and much smaller places can serve as hubs to other places of interest as well. I've done hub/spoke stays of 5 days or so from places most Rick-fans probably never heard of. Osterspai? Bullay? Neustadt-an-der-Aisch? Herleshausen? Rilchingen-Hanweiler? Steinach (Schwarzwald)? Staying in smaller towns - on farms, or with a winemaker, or in a castle-hostel, or in a family-run inn - does not mean automatic isolation from the rail network or larger cities. And you get a very different perspective by staying in such places. You might consider one or two small-town hubs during your month-long visit. For me, coming back to the same big modern city for several days is fine for a while, but I think a plan that repeats that routine in 3 separate large cities over 30 days makes for a narrower kind of experience.