Hi Regina- I'm an expat living in Lima- 10 days is a amount of time for a taste of Peru. You could thoroughly explore the Sacred Valley in that time (there is a lot to see) or you would have time to add on Arequipa or something else if you'd like.
I've enjoyed living in Lima (especially for the food scene), but it's definitely skippable on a short trip. As others have recommended, going directly to the Sacred Valley is the way to go. Once you land in Cusco, try to get to lower elevation as quickly as you can- it's about a 2 hour drive to Ollantaytambo, which is a good base for a few days. Then you could move on from there to Aguas Calientes/ Machu Picchu and work your way up back to Cusco. Cusco needs 2-3 nights. Book your Machu Picchu tickets before you book anything else, because they can sell out quickly for your preferred routes. I'd suggest going to MP twice- one in the afternoon the day you arrive, and one early the next morning. If you get a 6am or 7am ticket, it's magical without the crowds. Don't linger in Aguas Calientes- one night is fine to maximize your MP.
This would be a good time of year for the Amazon, on Puerto Maldonado or Iquitos are both easy flights from Cusco. I haven't been to Puno yet (I've lived here about a year). Another option would be to fly into Chachapoyas and go to Gocta Falls with a day trip to Kuelap (haven't been here yet but am going next month, and I've heard great things). Kuelap is still being excavated and is about 1000 years older than Machu Picchu.
The Sacred Valley is a highlight but there's a lot to see. Peru is also very easy to do independently- it's safe if you stick the tourist routes and has good tourism infrastructure. This woman lives in Cusco and I've found her blog very helpful: https://heatherjasper.com/