First - do the trip.
Second - Prepare for it and you'll be fine.
Third - The Oday 30 if well maintained, is fine for the trip.
Fourth - Have recent charts for every inch of the transit.
Fifth - Be in by 1500 to avoid t'storms (but not as common as in the Chesapeake)
Now for specifics.
I grew up in Ocean City, NJ and sailed my father's Catalina 30 from OC to Newport, RI with two friends when I was 20. I've also done the OC to Annapolis trip several times (we're on the Bay now). We went directly from OC to Block Island deadrecon-ing (it was 1978 and we didn't even have Loran). For purposes of the thread, I won't recommend this route and will stress that for a new cruiser, I'd only go in summer when weather is mostly fair. Assuming that you want to stop at night, I'll give you our return itinerary. From Cape May, your only real option is to stay about 5 miles offshore until you get to OC or head another 5 miles to Atlantic City. There is nothing in between that's safe (except maybe Townsend's Inlet). OC's inlet (Great Egg Harbor) can get bad in bad weather, but on a good day, is easily navigated (my brother-in-law does it weekly in his CD-25D). AC is a much easier entrance, but the slips are pricey from what I hear.
From AC, you can make a long day's run to Manasquan. It's a small harbor but holding is good. I've not been into Barnegat, but it's entrance can be bad. As with OC, Bernegat has quite a bit of local traffic so it's manageable in good weather with local knowledge.
Frome Manasquan, it gets tricker. You can go all the way through NYC to Manhasset Bay where you will definitely be one of the smaller boats, but it's fun if a bit pricey. In NY harbor, keep a keen eye for all sorts of traffic. Not difficult, but follow the rules of the road, stay out of the way, and definitely get a tide chart for the East River (can run ~3kts).
From Manhasset Bay, you have lots of options on the LI Sound. Decide how long you want to transit and pick a stopping point from your Coast Pilot (get one) or Chartbook. We stopped in New Haven and New London. Beware of of the "Race" which is roughly between Montauk Pt and New London. LI Sound narrows at at the Race and if you have a falling tide and an East wind the water can get BIG. An anecdote: we transited westbound in 20 kts going downwind with no reef in 8' seas at 12+kts. We broached, gybed, blew the goosneck apart and tore the main 4' up the luff. I learned to sew that day. If the weather is up, stay in port or I think tha you can go behind Fishers Island but will defer to anyone who has local knowledge.
Go to Block Island. It was magical. I hope that it hasn't changed, I haven't been back but want to.... VERY cool place. You'll anchor in the Great Salt Pond. Have a motor or strong arms. Not sure if there is a marina with slips. There wasn't when I was there.
Newport is a must-stop. Annapolis of the north. Try for reservations before arriving at a mooring or in a marina. Otherwise, it can get real crowded. Newport is a far north as I've been so I have nothing further to offer.
Good luck, it's a great trip
and very feasible. Out and back took us two weeks but we were rushing and did some very long days.