I'll list some I'd definitely recommend (below are in no particular order):
1. Mt. Teidi & Parque Rural de Anaga (Canary Islands). Teide's more of a personal challenge (3rd highest volcano in the world) but has a beautiful hiking trail throughout (especially in the lower areas where vegetation still grows) and takes around 6 hours just hiking down from the peak. Anaga Park is a stunning old-growth forest in the northern part of the island rich with wildlife and black sand beaches near the sea. All the other islands near it (and accessible by ferry) are also unique and definitely a must-visit (like La Gomera).
2. Abruzzo National Park (Italy). Forested mountain landscape with lakes, streams and waterfalls scattered throughout. One of the few places in Italy the Italian Wolf is still present in.
3. Marinello Lake Reserve (Sicily). A reserve with protected lagoons and within close proximity to the sea (that you're allowed to swim in). It runs along adjacent to cliffs of approximately 50-60m in height (IIRC). It's a short 1-2 hour hike visiting the reserve, but there's other hiking paths nearby like Galleria pedonale that can be merged with it. It's also really cheap.
4. Suserup Skov (Denmark). One of the oldest forests remaining in Denmark.. It's a really nice location albeit it's quite a short hike. NB: Denmark has a lot of hiking/green areas, however, they're heavily managed and quite "artificial" due to said management.
5. Dolomiti Mountains (Italy). Literally a picturesque landscape. Frankly all the mountain ranges from northern Italy, Switzerland and south-eastern France are all stunning, irrespective whether you're trying to go through Turin, Milan, Geneva or Marseille.
There's obviously a lot of other places like the Black Forest (Germany), but I listed the top 5 from my personal experience/memory