Drive the Adriatic coast

Along the Italian peninsula or through Croatia-Montenegro-Albania?
Both are possible.
In Italy you would drive to Brindisi, then take a ferry to Patras.
Along the Balkan Peninsula the fastest way, on the freeway, runs through the interior so you won’t see much coastline. Also rental car companies often do not allow to go there through former Yugoslavia. In any case you need to request because they might also be restrictions on your ability to load the car on the ferry Italy-Greece.
There are also huge one way drop off fees if you plan to pick up the car in Milan and drop the car off in a foreign country, especially as far away as Greece, as the company would need to reposition the car in Italy.

Aside from the prohibitive costs involved in such a trip by a rental car, October is the wrong time of year weatherwise to be driving on the Adriatic coastline.
This is when the high winds of the Bura move in along with rainy days. The deteriorating weather that starts in October is why hotels, restaurants and tour companies begin shutting down their operations in both Croatia and Greece at that time.

The area around Trieste and south would be affected the most by the bora winds, but it's not a frequent event, maybe 15 days a year or so, and especially during cold spells.

If you take the Italian coast route, and go to Brindisi (Puglia) to take the ferry, therefore Milan > Bologna > Rimini > Ancona > Pescara > Bari > Brindisi, the bora is not an issue at all, and the weather is generally great throughout the Adriatic coast in October.

Be aware that most rental agencies, although they allow to take the rental car on a ferry within Italy and the Italian islands (like Sardinia, Sicily, Elba), will require special written permission to put the car on any international ferry to Greece or anywhere across borders. Failure to do so will invalidate your insurance coverage.

I wouldn't take the eastern coast route via the Balkans because you will need to pass through Eastern non EU countries, like Montenegro and either North Macedonia or Albania, and most international rental agencies strictly prohibit that because of extra insurance requirements and theft concerns. Even if they give you permission they will add major insurance fees to cover you outside the EU.