The atlantic ocean is a big place - have anything special in mind?
I'm assuming you're driving...
Maine that time of year is beautiful... northern maine is still relatively affordable-- but it's a hike from Ohio) and unless you are part polar bear - the water isn't really swimmable until August...
Portsmouth New Hampshire is also nice... and on the water - though a little bit pricey...
Cape Cod and the surrounding areas of Massachussetts are beautiful - but that time of year, is gonna be steep (though if you aren't looking for five star accommodations, do-able...)
The Jersey Shore (my favorite place on earth) (that's the New Jersey Seashore, not jersey shore, Pa) has some places that are affordable if you stay during the week... you might find some cheaper motels (nothin' fancy, though some have a kitchenette) for your price range.. If you go to hotels.com, and search on asbury park for the city... there's a travellodge in wall township for 117 a night (with a fridge in the room) Wall township will take you close to the ocean (it's a stones trhow from Spring Lake - which is l ovely)
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