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I'm looking for trekking suggestions in the Western European time zone or the western hemisphere in the last week of May. I've got a week to figure out where I want to go because I learned last week I'd be able to take a couple of weeks off of work.

I was thinking about Jotunheimen in Norway because of ease of access, relative safety of the country, clean water along with lots of hikeable summits and great infrastructure that makes it easy to solo. It looks like there's still a fair amount of snow at that latitude and altitude though. It's not quite hiking or ski touring season there. It's somewhere in between. I thought about the Cordillera Blanca but it looks like the same problem might exist for Peru's treks and I can't find any guided summits that line up with my schedule.

Is there anywhere good to go for a 7 day trek at this time of year?

Hi ddreg0

If you want you may check several nice trekking routes in Greece.
you can combine nice forests, rivers, waterfalls ...and even sea!

Feel free to check this website which has good description from various mountains in Greece.

https://olympusmountaineering.wordpress.com

Finally, whatever you might decide to do, have fun and be safe!

Try the watery canyons of Utah or the area around Arequipa Peru. Late May is the prime season for both locations.

I know well both Jotunheimen and Cordillera Blanca, i am confident that both areas are suitable for trekking starting from the end of June/mid-July. I suggest you a couple of ideas: the GR20 trail in Corsica and Alta Via delle Dolomiti n. 1.
Have fun!

I agree with Silvia that the Alta Via delle Dolomiti n. 1. is also a great one too