The cost will be under US$20 in a taxi and that is the best way. You buy a ticket from a booth at the airport based on your destination. I would not reccomend a hotel near the Basilica. They are pretty basic. Stay at the Hilton Alameda or Crown Plaza or Embassy Suites. The taxi literally will go straight to Reforma and you wlll be near your hotel for easy access each day.
THe Basilica itself is free. There is a large plaza and you go to the newer church where one goes down a ramp and then sees the miracle from a moving walkway. The church is very large and masses are said. There are several historical churches in the compound and there is a hill (steep for an elederly person I would say) to walk up to the original church. Maybe the elderly person could enjoy people watching at an outdoor area with statues of the miracle and others go up the hill.
You can buy religious souveniers, plus candles to light and there is a snack bar area.