The names of these hotels can make referencing them confusing: Courtyard Rome Central Park, Rome Marriott Park Hotel, Courtyard Rome Airport.
My brother-in-law checked in to the Courtyard Rome Central Park on points last week. He found the hotel to be unacceptable in terms of the Rome experience that he was looking for. It's not exactly in central Rome, but in his words, a "hotel greatly in need of some maintenance and a face lift, located in an unattractive neighborhood." Also, there is train access to central Rome from the hotel (line FM3), but the trains stop running at 9pm. Fortunately, a call to Marriott yielded a points refund for the rest of the reservation period after that first night, and the next day he was able to transfer to a stay at the Boscolo for two nights on points (all that was available on points, spur of the moment) and a paid stay the third night. For the fourth night, the Boscolo was booked solid (as was the Grand Flora), so they stayed with us in our suite at the Grand Flora that night, which was perfectly fine for all, as the suite was spacious. Super duper hats off to Marriott and the Boscolo for helping make that change happen for them, and hats off to the Grand Flora for allowing 4 persons to stay in a suite for one night.
To be clear, the Courtyard Rome Central Park is perfectly fine if budget is the prime factor, but the limited train hours of operation could indeed be problematic to my mind.
As far as needing to stay at the airport Courtyard, I have stayed there (7 years ago), and I found it to be perfectly acceptable, however this trip I learned that it is very easy to either take a taxi to/from Fiumicino (the regulated rate has recently been raised from 40 euro to 48 euro) or the Metro/Leonardo Express train (1,50 euro for the metro, 14 euro for the Leonardo Express), however this train doesn't run 24/7. I took the Leonardo Express from Fuimicino back to the Grand Flora after seeing my daughter off early one morning, but the first train from Fiumicino didn't start running until 6:38am.