We are a planning 9 nights with 3 nights in Lisbon and 3 nights in Porto. I am thinking to do that the first 7 days and then while heading back to Lisbon, stay a night in Coimbra and a night in Sintra and the last night in Lisbon. Does this make sense? Can it all be done by train or would it make sense to rent a car in Porto to drive back? Thanks for your input.
I haven't been to Porto and Coimbra, so I can't comment on those, but Sintra is a very short train ride to/from Lisbon. (About a half hour, if I recall correctly.) You would want to stay at places that will let you store your luggage either before check-in or after check-out, since there is usually a 4-5 hour gap between the two, and you probably wouldn't want to haul your luggage around during that time.
I forgot about the luggage! So if we did an overnight in Coimbra then went to Sintra before returning to Lisbon for the last night, we would just need to find a spot for our bags while in Sintra. Anyone have ideas? Is there luggage storage at the train station?
I would rent a car so you can explore more places. Look at Alcobaça and Obidos, Evora.
Why not stay your last night in Sintra? That way you don't need to worry about luggage and can also see it after the day-trippers leave. I would not bother with a car for this trip. You have good trains between Lisbon , Porto and Coimbra and enough to see if those 4 sites for 9 days.