When you are going can make a difference on what to expect especially for services.
I go to Greece either spring or fall and find it much quieter in most areas including islands.
I've been going to the Peloponnese the last three trips as I find it has just as much to offer as any island and more.
Nothing wrong with islands as I've been to many but some have become way to popular and over touristed especially during high season.
With 15 nights you could do three locations as a base to explore each area.
You seem to be mostly interested in the south of the peninsula which is a good choice.
However there are numerous other areas worth exploring but maybe another time.
I spent 6 nights in Gythio which is a lovely waterfront town not overly devoted to tourism and a great base to explore the Mani including the tower villages like Vathi, day trips to Mystras and even Monemvasia.
I spent 5 days in the little known Petilidi and was a great base to explore the Messinia area including one of the best and least known archeological sites in Greece known as Messini. Spectacular setting in a rural area and much still standing. Very neat, well organized and extensive. Also went into the interior mountain areas for day trips.
Pylos was just OK for me but found Koroni much to my liking. Nice waterfront and lovely hillside village.
You asked about the town the French designed after Greece won it's independence from the Ottoman Empire. It's Methoni but in the southern part of the Peloponnese and south of Pylos and yes it has a more European "look" with straight streets and laid out in a grid-like pattern. It was OK but I stopped there to explore the old Castle/Fortress which is impressive.
The Peloponnese is a great alternative if you've had your share of islands. The best guide is the Cadogan Guide and even though last published in 2008 it's still the most comprehensive and encompassing of any other guide book. Only available as a used book from abebooks or even ebay. It's worth whatever the cost is but I got my a few years ago at a low price than what's stated now.
Anyway enjoy the Peloponnese and do your research!