10 days in chile

My wife and I are planning a trip to chile in MId March. We will be in LIma for a few days then off to Chile. We have about 10 days to explore. We will travel by any mode of transportation that makes sense. Does anyone have a possible itinerary?
Thank you for any help you can give.

I'd completely skip Lima, or at least remain there for as short a time as you can get away with. There's nothing of any interest whatsoever to see, and if you only have such a very limited amount of time, you'd be much better off spending all of it in Chile (or somewhere in Peru which isn't Lima). Additionally, mid-March is the end of the wet season in Peru; again, you're better off further south in Chile where it's just early-autumn.

The distances involved are huge, too. What do you want to see in Chile? Unless it's the desert in the north, you'll probably just want to fly there from Peru. (The alternative is a long bus ride; I wouldn't recommend renting a car yourself.)

thanks for the quick reply. We just wanted to go to Machu picchu in Peru. That was it. In Chile we woud like to see some historical sites along with the traditional tourist spots. However if you have real gem to visit that is of the beaten path we're not opposed to that either. We would want to finish off the last two days lounging in a nice place on the coast.
we will just carrying a backpack so we are fairly mobile.

You unfortunately can't just nip over to Machu Picchu due to the altitude, for which you need acclimatization at lower heights for several days first. *ponders* Although Machu Picchu itself lies low enough (at 2400 meters) that you can probably go straight there. It's just Cuzco which is the problem due to lying at 3300 meters... so if you could fly into Cuzco and train straight out to Aguas Calientes on the same day, that would probably work out okay, with you at most having a severe headache as a result. Would need some tight planning, though.
Otherwise Arequipa (at 2300 meters) is the most common halfway there stop, and quite worth seeing in its own right.

For Chile itself, I only ever stopped over shortly in Santiago, so I'm afraid I don't have recommendations there. I'm sure other people will be along shortly who do have recommendations, though.

Pucon is a town about 10 hours south of Santiago by bus. I loved it there. Very much similar to Bariloche. Amazing lakes, volcanoe's, lot of exploring to do and plenty adventure activity such as scaling the volcanoe's and sledging down, rafting, canyoning, cycling, hiking.

Plenty good places to eat and stay there too. The best ice cream I have ever had and chocolate to die for.

My fav place in Chile is defo the Torres del Paine National Park so if you have the inclination to get there and trek for 5 days then go for it. You won't be dissappointed.