Based on your interests, here is a suggested 5-day itinerary for the Azores:
Day 1:
- Arrival at the Azores
- Visit the historical site of Angra do Heroismo, a UNESCO World Heritage Site on Terceira Island
- Explore the local cuisine with a traditional Azorean meal
Day 2:
- Hike the Pico Island, climbing the highest peak in Portugal and enjoying the stunning views
- Visit the vineyards and wine cellars, tasting the local wines
Day 3:
- Travel to São Miguel Island
- Hike the Sete Cidades Volcano, exploring the twin lakes and the beautiful landscapes
- Visit the Furnas Valley, experiencing the unique cooking method of the geothermal steam
Day 4:
- Hike the Levada do Caldeirão Verde in São Miguel, a beautiful trail through the lush forest
- Visit the hot springs and natural pools in the area, enjoying a relaxing afternoon
- Enjoy a seafood meal at a local restaurant
Day 5:
- Visit the historical sites and museums in Ponta Delgada, the capital of São Miguel
- Explore the local markets and shops, purchasing souvenirs and traditional products
- Departure from the Azores

This itinerary covers a mix of hiking, historical sites, local cuisine, and beaches, ensuring a well-rounded experience in the Azores.
Citations:
[1] https://google.com/maps/?ll=37.741249%2C-25.675594&q=Azores&z=15
[2] https://www.geekyexplorer.com/hiking-azores/
[3] https://gretastravels.com/hiking-in-the-azores/
[4] https://www.foodrepublic.com/2016/07/18/azores-food-primer-10-essential-foods-and-drinks/
[5] https://www.indietraveller.co/beaches-and-pools-on-the-azores/
[6] https://trails.visitazores.com/en
[7] https://www.foodandwine.com/lifestyle/what-eat-and-drink-azores
[8] https://bookatrekking.com/en/blog/hiking-in-the-azores/
[9] https://www.portugalist.com/azores-food/
[10] https://globaldebauchery.com/azores-beaches/
[11] https://wanderlustcrew.com/the-azores-food-guide/
[12] https://www.ohmycodtours.com/blog/azores-food-and-wine-guide/
[13] https://www.magical-azores-islands.com/Azores-Beaches.html
[14] https://adventure.com/the-best-hikes-the-azores-portugal-trekking/
[15] https://www.geekyexplorer.com/azores-beaches/
[16] https://www.muchbetteradventures.com/magazine/hiking-in-the-azores-a-guide-to-the-best-hikes-in-azores/
[17] https://trails.visitazores.com/en/trails-azores
[18] https://www.viator.com/Azores-tours/Historical-and-Heritage-Tours/d22379-g4-c12
[19] https://www.reddit.com/r/azores/comments/180tzs1/sao_miguel_beaches/
[20] https://whc.unesco.org/en/list/?order=country&search=Azores