Working downward, toward the present day, is harder.
The first stop would be the US Censuses. All of them are at familysearch.org. It's free to use, but you need to set up an account.
The 1840 census only lists heads of households, then composition by sex, age, and free vs slave. 1850 to either 1860 or 1870 list members of the household, but no relationship stated. After that, relationships are included. The information asked on the census varied from decade to decade, read all the columns.
You probably aren't going to find a lot of vital records. Some places recorded them in the 1800's, but they weren't required in the US until about 1900, someone else knows the exact year, I'm sure.
If you figure out where they settled, there are lots of newspaper archives online. Look for County biographical histories also. And there are some good rootsweb and genweb sites still around for some of the counties. (and some not so good.)
Which brings us to the main point, Philadelphia was a port of entry, and although they could have stayed there, they could just have likely moved westward. If not immediately, then from generation to generation. But you can probably eliminate their going to New England or New York, or they would have entered through a different port. Likewise maybe for the far Southern states, but I'm not positive. My first guess would be that they ended up in Pennsylvania or Ohio somewhere, Maryland, maybe. - I'm basically drawing a line west from Phila and seeing where it goes.
Were other families obviously traveling with them? Track them too, they might have gone to the same place.
Watch for varieties in spelling, just as in Ireland. Donahoe could be Donahue, etc.
And a long, long shot, do you know where they were from in Ireland? I've worked on a Donahue family in Pine Township, Pennsylvania, who were from Co. Tyrone. The immigrant was Hugh Donahue, b 1789, married to Susan __, the children were born from 1821 onward in Pennsylvania.
