I've been to all the places you list and have never rented a car in Europe. You will have no difficulty at all in most of those places. In a few (including Provence and parts of mainland Greece) you may find it awkward or impossible to directly link one very small town with another, which can require extra time, use of private transportation (like a taxi) or removal of a spot from the tentative itinerary. However, you do not mention any small towns in your original post, so it appears you may not plan to go to any problematic places.
The devil is in the details, so you really need to dig into guidebooks and be more specific about what ground you want to cover. All non-rural parts of Europe are accessible without a car, and you can get around even most of the rural parts to some degree, even quite small towns, by train and bus if you're selective in which small towns you choose. It would be more efficient to ask which parts of Europe are challenging or impossible without a car than to ask whether you've missed any that are perfectly fine to visit via public transportation.
Additional research should be done before you buy your flights, because I'm pretty sure you're going to discover lots more great stops in those areas (Seville, Cordoba, Granada and Toledo in Spain, just as one example), which will push the full list to more than 90 days in the Schengen Zone. I suspect you've got two trips there rather than one.
Places you haven't mentioned where I did feel constrained without a car included the Dordogne in France (though I still got to all but a few microscopic villages I would have liked to see, and that was partly due to limited time rather than total lack of transport), western Scotland (where you can't respond to sub-optimal weather very well without a car), and--for a future trip--the fjord country in Norway (where I can see I'll be spending extra time since I'm depending on public transportation--and that's costly in Norway because lodging is very expensive).