We had plans to visit Monsanto when we were in Portugal last year, but never made it because it was 2 hours from our hotel, Parador Casa da Ínsua in Penalva do Castelo. It is a very nice hotel that we spent two nights at. We’ll visit Monsanto this year getting to it from Spain. From Penalva we visited Viseu and Lamego. The highlight of Lamego was climbing the 600 steps up to the small Santuário de Nossa Senhora dos Remédios.
Places we visited between Lisbon and Penalva do Castelo included Óbidos, Nazaré, Fátima, and Tomar. From Tomar we visited Almourol castle.
Óbidos is an hour drive from Lisbon airport while the beach town of Nazaré is only 20 minutes or so further. In Nazaré we stayed at Hotel Magic. It has its own nearby parking garage and it was free. Between Óbidos and Nazaré is Alcobaca monastery. It’s worth visiting, but probably not on arrival day.
Since you will have a rental car you’ll probably end up on some toll roads. Some tolls are all electronic while with others you still need to take the ticket and pay when you get off. Ask the rental company how it works. We rented from Madrid so didn’t have a transponder.
Prior to going over look up free parking lots in the towns you intend to visit and bookmark them to Google maps or navigation system. That way you can go straight to them saving you time. Other than Porto we didn’t pay for parking our entire trip.
Finally, there were a number of places that were cash only, more than most other countries I’ve recently been to, so have some on hand.