I visited Ayder and Trabzon few years ago and happy to share my itinerary.

Day 1: Land at Rize or Trabzon airport and head straight to Ayder Plateau, around 2 to 2.5 hours drive. Skip Trabzon city unless you really want to see it or if you arrive late. You will find lot of hotels in Ayder, those who are close to road are easy to access, some high up need some uphill walk but then you are rewarded with even better views. 

Day 2: After breakfast, you can either rest and enjoy Ayder or book a jeep and do half day tour to Zil Kale, a beautiful old castle sitting on a cliff and a nearby waterfall which is beautiful, on your way you will see few old ottoman bridges, ask driver to have a photo stop. In afternoon book a jeep and go up to Huseyr, a hilltop where you’ll literally be above the clouds. The road is rough, so an off road experience,  not for the faint-hearted, but the view is amazing, highly recommended if you dont mind the off road experience for 25 to 30 min . There’s a restaurant at the top for snacks and tea.  

Day 3: So we booked half day castle and waterfall tour next day as did not want to pack both trips in one day. Castle views were amazing. In afternoon we left for tea plantations and then checked into Ridos Thermal Hotel for the night. The natural thermal water is full of minerals and very relaxing. 

Day 4: Travel to Uzungöl, the famous lake surrounded by mountains. It’s very commercial with lots of hotels and tourists, but still worth seeing. If you stay overnight, pick a place up in the hills for quieter vibes and better views. You can also ask a local driver to take you on a tour of 5 or 7 nearby lakes hidden in the hills less crowded and more raw nature.

Day 5: If you're interested in history, you can visit Sumela Monastery, a famous site built into a cliff. Otherwise, just take it easy either enjoy a slow morning in Uzungöl or make your way back to Rize or Trabzon before your flight.

Good itinerary, however I would like to add a gem not far from Ayder, its called Pokut Plateu.

While Ayder is a beautiful green paradise on its own, Pokut is something else, a high altitude wooden village sitting above the clouds, reachable only by off road jeep, and it gives you a feeling of being far away from the world.

The drive to Pokut is bumpy and adventurous , but once you’re up there, you’ll understand why people rave about it. The views are stunningrolling green hills, traditional wooden houses, and if you're lucky, clouds floating below you like a sea of mist. It feels untouched and peaceful, like stepping into a postcard.

You can either do a day trip to Pokut from Ayder but i will recommend staying overnight. You'll need to hire a local 4x4 driver who knows the road well, my ayder hotel manager arranged the driver.

If you’re heading from Ayder to Uzungol you can stay at Ridos Thermal Hotel near Ikizdere. It’s surrounded by green mountains and famous for its natural hot spring water perfect for relaxing after a long day. The whole area is known for tea. The tea factory is perhaps 10 min drive and has a restaurant where you can sip fresh tea and enjoy plantation view.

We booked a tour from uzungol and driver took us to few lakes high up in mountains. You can book tour from hotel as most of the hotels offer it.