We will be gone for 25 days and are going to Rome (1 day), Amalfi, Naples (1 night before our flight), Mykonos, Santorini, Athens, Lisbon, London, Paris and Barcelona (1 day before our flight.)

What are some non-touristy things we can do in each city (we've been to the majority and want to do something different this time.) So far I was thinking:

Rome: We're only here 1 day and last time we were here the Trevi fountain was closed. So we were thinking of going there.

Amalfi: We will be renting a car and driving from Rome to Amalfi. I believe we will stop at Pompei along the way (is there parking?) We also want to take a trip to Capri.

Mykonos: So far we're just planning on going to the beach.

Santorini: Beach, Caldera, etc. Can anyone recommend a place to rent quads here or in Mykonos?

Lisbon: I know we want to take a day trip to Sintra.

Other than that we're not sure.

Also, how much money should I budget? We have already paid for flights, hotels, and transportation between cities. So basically just food and transportation within each city (although we don't mind walking!)

Any other information would be greatly appreciated, Thanks!