Wife is from Iowa (Dyersville) and I've taken her to NJ a number of times. I'd echo those recommending Princeton and the Jersey Shore. Hoboken is very nice as well if you want those big NYC views, along with a lot of restaurants and a vibrant bar/restaurant scene.
Princeton has a beautiful and historic campus which is worth seeing and is a manageable, clean, fun town to grab lunch/dinner.
As for the Shore, it kind of depends what you want. If you want to get your feet wet in the ocean and go for a walk on the beach, I would probably recommend Sandy Hook/Sea Bright along the northern part of the shore. Weather should be ideal late September, water won't be cold, and I would think you would enjoy it. If you want Jersey kitsch, you can hit Pt. Pleasant or Asbury. Both have boardwalks...Pt Pleasant, that time of the year is likely to be more quiet, while Asbury has a bit more of a year-round vibe there. Asbury is a little more 'eclectic' with hipsters and tattoos and that sort of thing, but also some really neat buildings from the 'glory days'. If you want quiet, upscale Jersey Shore, check out Bay Head (just south of Pt. Pleasant) which have a bunch of big shore homes and a small downtown with a few restaurants. Ocean Grove is also an interesting place with some neat architecture and a nice beach to walk as well. If you don't want to work hard, Pier Village in Long Branch is fine...has a boardwalk, some restaurants, parking, and is on the ocean. For what it's worth, my wife loves Bay Head, is so-so on Asbury, and likes Sandy Hook/Sea Bright.
If you are into history, there are a ton of things to do as well due to the Colonial history of the area...but I'll let others fill you in on that if interested.