Leaving aside that your opening words are
I am planning to drive from London to Georgia.
We don't know enough about you to be able to tell you about good places to stop on the route from Greece. On route planning software from a nominal start point of Athens the route skirts Thessaloniki (to me a crying shame, but you may know the city well).
Then neither obvious route takes you anywhere near Gallipoli. In the theoretical circumstance that I was making this journey my interests could not let me miss Gallipoli for its WW1 history, but that could not matter to you.
Then on the direct route you skirt to the north of Istanbul/Constantinople. I couldn't possibly miss a few days in Istanbul, but have to dip well south to do so. To me on such a journey I would be visiting Constantinople whatever the map calls the City.
My knowledge of Turkey is very basic, but the direct north coast route does not look hugely interesting to me.
I would be more interested in dipping south to route via Ankara, adding on about 350 miles worth of driving.
But if I'd been to Gallipoli I would then want to do the south coast on the way to Ankara via the likes of Izmir and Antalya. That route I believe is more like one of the former Old Silk Road routes, but then to Georgia you are diverting to another of the more northern Silk Road routes.
Also I personally couldn't miss Lake Van and then Mount Ararat. However Lake Van is taking you towards Iran. From Lake Van the 'problem' is you would then it seems have to enter Georgia through Armenia. I say problem advisedly as that should be a very interesting diversion in it's own right.
But you get my drift- you can either do this as an A to B route as fast as possible in around 35 hours of driving (4 to 5 days) or do it as a road trip in which case there are all sorts of deviations, depending on one's interests.
The Silk Roads have long been a fascination of mine, so if I was doing it I would rather take 70 or 100 hours or whatever it takes, to build that in, as well as Turkey's great archaeological sites.