I'm likely planning ~10 day trip in Greece (including travel) in early October. I prefer more budget accommodations, would love a day or two on a beach (or boat!), and prefer more active types of activities if you can DIY (national parks, hiking, sea kayaking).
Any suggestions for an itinerary or must-see places?
Greece is such a big country ant there are many many things to see and do. Since you're into more adventure stuff I will skip the islands part!
First and foremost you should check out the website of Trekking Hellas, which is a well known "tour operator" for avtivities like hiking and kayaking http://www.trekking.gr/sections/outdoor-holidays-in-greece
We don't have National parks in the essence that the US has though. A few places I can think of is Mytikas, Mt Olympus which is the tallest mountain in Greece (an supposedly where the ancient Greek Gods resided). Mytikas is the top of the mountain but you don't have to reach up there...there are other trails as well. Here's the website of a company that specializes in hiking up Olympos Mountain http://olympostrek.gr/index.php?lang=en
then there is Crete and more specifically Samaria Gorge which is very interesting to visit. While in Crete you can also visit Chania, Rethimno and Heraklion. Here's the website for Samaria Gorge http://www.samaria.gr/language/en/
Let me know if you need anything else!
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See Thessaloniki, the hidden treasure < the best city i know in Greece.