I doubt there are any direct "public" transportation options. You should check www.amtrak.com to see about getting to New York Penn Station or Newark Penn Station and then taking NJ Transit or asking your sister to pick you up if Newark).

Actually, New York Penn Station would be better than Newark Penn Station in case you can't be picked up at Newark Penn. NJTransit offers direct service to South Orange on the Morris/Essex line from NY Penn, but not from Newark Penn, which is on a different NJTransit line. The trip from NY Penn to South Orange takes about 35 to 40 minutes. Frequency (no more than hourly) varies with time of day and weekday/weekend. Be sure to purchase your NJTransit ticket from a vending machine at NY Penn; there's a $5 surcharge for tickets bought on board. Your 6-year-old rides free. Connection at NY Penn is relatively simple, involving ascending a flight of stairs (some platforms have escalators and/or elevators), then descending to a different platform.

Yep, pretty easy to do as described above. The South Orange train station is right in the center of town. Many folks commute by train from there to NYC every day. If you don't mind paying the extra cost, the Acela from Boston to NYC would be a nice way to go.

Can we drive most of the way (I just don't want to drive into the city) and then take the train the rest?

Wouldnt you just stay on 95 through the Bronx & then into NJ? What are you trying to avoid?

I'm not sure I understand why you would drive part way. From your description it seems like you are trying to avoid driving "into the city"--do you mean New York City/Manhattan? You can drive from Boston to South Orange without traveling through New York City--look for routes over the Tappan Zee Bridge. Even the more southerly, faster route through the Bronx over the George Washington Bridge should be no worse than Boston traffic.

Otherwise, as mentioned, easiest would be Amtrak from Boston to New York Penn Station. Then switch at New York Penn Station to new Jersey Transit to South Orange.

If you're driving directly from Boston to South Orange, there's no need to enter New York City. I suggest you consult Google Maps or MapQuest to seek driving directions. You can alter the suggested routing, if necessary, to avoid NYC.

Boston to Tappan Zee.
Tappan Zee to Garden State Parkway.
Garden State Parkway to (as the sign says) The Oranges.

If you are leaving from Boston or north of Boston, take the Masspike to 84, then 91 from Hartford to the Wilbur Cross Parkway, then that and the Merritt Parkway to 287. No trucks on the Parkways. 287 takes you across the Tappan Zee.

If you are leaving from one of the southern suburbs, it is more effective to suck it up and take 95 all the way to 287 and the Tappan Zee.

The Garden State Parkway heads off I think three exits after the bridge, there is a rest stop within a mile or two after you enter where you can use the toilets, go to the food court and buy gas if you need it. No trucks on this parkway either.

Don't buy gas in CT or NY if you can help it.