well welcome to the site
I am also from PA, the NE part of the state
as for is there good public lands in Ohio near the border
well guess that might come down to what part of the PA border
but over all, YES and NO
many public lands close to the border, or my experience, get hunted harder, due to many folks that hit two states, tend to stay closer to each hunting area, thus making border area's get more pressure
Ohio DNR web site will lest most all public area, so go look there
Ohio is a GREAT state, with GREAT hunting
like all hunting
there are not monster bucks behind ever tree there
you have to do your part, but there are big bucks there in a higher percentage than here in PA
I've never taken an archery safety course, and was never asked about one buying a hunting lic in Ohio
BUT I am a much older person, and in many states I don't even have to prove a hunter ed card because of age, as yrs back wasn't needed!
so I would suggest calling the ohio DNR and asking them, to get the correct answer over just someone word on a forum
I have hunted in about 15 states
be glad to share some info on some great hunts I have done, all DIY hunts, found some super deals too along the way
I've hunted MY too, near the bay, tons of BIG bucks down that way, but access to land is very hard to get, tons of big money clubs lease most and have high standards, thus why big racks
tons of corn and soybeans , and extra long growing seasons as to PA
I've also hunted in NY too
some great hunting up about Redfield, or I found a bunch in that area!
being a PA resident, I used to do hunts in Ohio,i'd Bow hunt ohio, the week after the PA bow season ended, for 7-10 days,
then hit WV opening day/ or a week for ther rifle season, and then be back in PA for Pa's rifle season
never then missing any days of hunting in PA!
a great way to make 3 hunts happen in one road trip
WV has liberal deer limits, and most area's near Ohio, have super high deer numbers
a good place to look to add a state to hunt in!