Hi!

I used to live in Lima a couple of years before moving back to Europe.
1) The exchange rate at the airport isn't best possible but neither rip-off. You can find Interbank counters all over the airport, the easiest and probably safest place to exchange money is at baggage claim. When withdrawing money, try not to use Globalnet ATM's, they are the only ones charging extra comission with foreign cards. Small US bills (especially 20 USD) in cash are widely accepted in Peru, they can be used at local supermarkets etc without problems (and some of them use interbank rates). You have always carry small change with you, don't expect that taxis etc have change!!!

2) There are no metered taxis in Peru, always negotiate the price in advance (if you a get a gringo price, just ask the next one like locals do). I have always used Taxi Green without problems. I think the current price to your hotel with them is 45 soles.

3) Your hotel is located in Miraflores which is probably the most recommendable & safest part of the city to stay overnight. As part of your day, I would recommend walk around in Miraflores and Barranco. Depending on your interests, you might want to visit Huaca Pucllana ruins in Miraflores (~15 minutes walk from your hotel).

Historical center is a bit far away from Miraflores but it's really worth visiting if you can find time for it. Given your time pressure, you might want to consider taking a tour to go there (tours can be bought at Parque Kennedy, ask from the reception where the tourist info at the park is located).The sunset close to Pacific is beautiful (there are many nice parks on the cliffs, less than 10 blocks from your hotel), don't miss it if you are in Miraflores/Barranco.

You can eat Peruvian meat dishes in the mountains so I would recommend you to eat seafood in Lima. The locals eat seafood mostly during the lunch, typically ~1-3 pm. The best known local seafood dish is ceviche (raw fish, if you like sushi, you will enjoy it) but there lots of other kinds of local dishes. Some of the well-known seafood restaurants in Miraflores and San Isidro are La Mar, Segundo Muelle and Punta Sal.

It's worth visiting Wayna Picchu but it requires hiking so it might a be a little complicated with small child... Those tickets are normally sold out in advance. If you want to see it, you should buy your tickets in advance (can only be bought when buying MP tickets). 1 day is sufficient if you take the first train to Aguas Calientes.

Your hotel seems to be very far away from the city of Cusco, in Urubamba, which might explain at least part of the price (I assume it's in soles)... Other Peru experts, might be able to advice you better with your Cusco related questions.