We were in Peru 3 years ago and did the following:

Lima (1 night): Belmond Miraflores Park (definitely a great hotel, but there are other options). We did dine at Astrid y Gaston which was amazing. The JW Marriott is also wonderful.

Sacred Valley (4 nights): Belmond Hotel Rio Sagrado. We loved the intimacy of the property and it cost less than the Tambo del Inka. We dined at the Tambo and it was a great dinner and nice property but definitely less boutique than the Rio Sagrado. But staying in the Sacred Valley is a great thing, making it easier to see many of the sites in the valley. We liked this property a lot, but lack of air con can be an issue for some. The salt mine was our favorite trip, and Ollantaytambo was also a worthy trip. Other trips were less exciting for us. The Pisac market was WORTHLESS--a scam to get you to buy crap that we don't need. We drove 75 min to reach Pisac only to be there 15 min before telling our guide we wanted to head back LOL.

Hiram Bingham train (both ways): We took the HB train from Rio Sagrado (pick up was literally just outside our door since it's Belmond train) to Machu Picchu and from Machu Picchu back to Rio Sagrado due to incursion on tracks--forcing us to bus back from Rio Sagrado. Depending on season there are limits to the route, so check in advance. I HIGHLY recommend the HB at least one way--the way up to MP during the morning allows you to see the beautiful views, but the way back from MP is the last train to leave, giving you more time to explore MP in the first place. It is pricey to do it roundtrip, which we can afford and loved, but for most people one way is more than enough. The food and service were wonderful, so if that's a priority the dinner ride back may be more worthwhile for some.

Machu Picchu (2 nights): Belmond Sanctuary Lodge. We LOVED it, partly due to the amazing Michelin level food (included in the exorbitant price) and partly due to the access in early morning and late afternoon without the crowds. We stayed in Presidential, which I don't recommend--not worth it. But not having to wait in line and then take the damn bus 30 min each way to Aguas Calientes to the Inkaterra was worth it alone for us LOL. The service and location and food made this a no-brainer for us....since MP was the biggest priority for the trip. We did hike up Huaynapicchu, too, on our second morning. Totally worth it. We chose 7 am over 10 am and got an amazing view of the MP site. The SL is overpriced, but still totally worth every penny LOL.

Cusco (2 nights): Inkaterra La Casona. We LOVED it. It was right next to MAP Cafe (in museum) which offers Michelin like tasting menus. Their 7 course Cena del Oro meal--which you have to request a month in advance--was better even than Astrid y Gason and Central! Hotel was across square from the Belmond Palacio de Nazarenas and Monasterio, so essentially same location, but just far more boutique. We had lunch and drinks at the Palacio and were VERY glad we stayed at the Inkaterra--which was more than half the price and far more intimate. But the Palacio is a nice hotel, more modern, more amenities in some ways. We despised the Monasterio, just way too touristy. We found this Inkaterra to be incredibly boutique with beautiful spacious and authentic rooms and tremendous service throughout. We'd return here in a heartbeat.

The more time you spend in the Sacred Valley, the less time you need to spend in Cusco (or vice versa) as a base to explore the Sacred Valley. Some people do one or the other, since you can reach both from the other. But we definitely appreciated the time to unwind, not feel rushed, and to explore each on its own.

M/V Aria cruise by Aqua Expeditions from Iquitos (7 nights). We recommend only doing 3 or 4 night cruise, but it was great. Service blunders here and there, and the food was just OK, but the experience of venturing directly into the Amazon was worth it. Swam with piranha, saw tons of caymans, iguanas, pink dolphins, huge lizards, birds, and even one anaconda. It was fantastic...for 3-4 days. The second half was largely a repeat of the first 3-4 days.

You also can do the Amazon by staying at the Inkaterra properties in Iquitos or Puerto Maldonado instead of doing the Aria/Aqua cruise. Either way, I highly recommend seeing the Peruvian Amazon--since it's higher quality and more luxe than seeing the Amazon in Brazil by far!

Lima (2 nights): Belmond Miraflores Park again. We tried to just change out flight to go home but couldn't, since we'd seen enough. But this allowed us to dine at Central and Malabar. Central was amazing.

I also concur that you should do Cusco (11000 feet) last of the Sacred Valley (9000 feet on average) and Machu Picchu (7800-8000 feet on average). That will help you acclimate to elevation and avoid elevation sickness issues. We went from Cusco to Iquitos, so what a change in climate that was!