Walk to Eastchester Road. Cross over to the other side of Eastchester Road and take a 238th St -bound Bx31 bus to Allerton Av. At Allerton Av transfer to a Bedford Park-bound Bx26 bus to the last stop (Bedford Park Blvd/Jerome Av subway station). At Bedford Park/Jerome Av, get a Westchester Bee-Line #20 bus to the Cross County Shopping Center.
To return just do the opposite: From the CC Shopping Center (on the side of Macy's) take theBronx-bound #20 bus to Bedford Park Blvd (last stop). Then take a Co-op City-bound Bx26 bus to Eastchester Road. Transfer there to a Westchester Square-bound Bx31 bus to Pelham Parkway. Then walk the short distance to the hospital.
The Bee-line bus accepts the NYC MetroCard (as do the the Bx31 and Bx 26).
From Jacobi, walk to the #6 subway at Westchester Sq, take that to 125th street, get an uptown 4 train to the last stop at Woodlawn. Look for the Westchester Bee Line #20 and that goes right to Cross County Shopping Center.
(Getting to the #4 subway you can also walk to Pelham Pkwy and get the Bx12 bus to Jerome Ave at the Fordham Rd. station.)
Here's how to get from Jacobi Hospital to Cross County Shopping Center.
Step 1 - exit the hospital and walk to the corner of Pelham Parkway and Eastchester Road. There you can catch the Bx12 bus westbound to Fordham Plaza, where a connection can be made to Metro-North's Harlem Line.
Step 2 - take the Harlem Line northbound from Fordham to Fleetwood. A round trip intermediate fare will cost you $5.
Step 3 - once in Fleetwood, transfer to the Westchester Bee Line. Take bus route 52 westbound from the train station to the Cross County Shopping Center. The fare on the Bee Line is same as on city buses, $2.25, and MetroCards are accepted.