We will be flying into Lima from Quito.we will have US dollars. I understand the exchange rate at the airport is bad and it is better to do currency exchange in city of Lima. Is there a way to get into Lima via taxi without exchanging money at the airport?

I think there are ATMs at the airport you can likely use.

http://taxidatum.com/taxi-fares-lima...cusco-airport/ Accept USD and are bookabke online. Green Taxi just outside the exit from arrivals is the official taxi service at the airport and I THINK accept usd. Alternatively, arrange transport with your hotel. It should cost $20-30.

As mentioned above there are ATMs available but I hesitate to use any in Peru that are not attached to banks and during opening hours for fear of my card being retained.

I think i am going to book with taxidatum.

I live in Lima and go to the airport constantly and I never heard about Taxi Datum....
Take a Taxi in Lima is not so safe, even the supposed official Taxi which is Taxi Green is a roullete. Taxi drivers are not evaluated correctly, and there are many thieves infiltrated. The safest way is asking for a transfer to your hotel in Lima and you pay it when you do check-out.
You do not need to change much USD into Soles, because US Dollars are welcome in Lima and Cusco, even in Aguas Calientes (Machu Picchu). And it is reccommendable to come with 2 credit or debit cards, in case one of them be retained in a ATM.

Taxidatum is a great service and needs to be booked online, not on-demand. I switched to them after a Taxi Green driver with a lead foot. You will get a meet and greet as part of the rate.

BTW there is also not an official Airport bus to Miraflores from the airport.

https://www.airportexpresslima.com/

Maybe not for everyone but if your hotel is near a stop it is an option especially for a budget/solo traveler. Tickets can be bought online or at the airport (both currencies) or onboard but no change.

There is NOW (not not) a bus ! Bad auto correct.