@Tammy Tebben I think a lot of the advice above jives pretty well with what you shared about your objectives. I'm guessing you could get some pretty good cash flow going down in Lancaster with your budget, maybe a couple properties with 25% down and keeping adequate reserves. Columbus is a great place to invest, but it's very competitive and cash flow is probably going to be harder to come by. Remington (above) is a highly recommended contact if you end up investing here.
There's a lot of be said, though, for investing in the area where you have the best competitive advantage and it sounds like that's probably Lancaster (less competition, more familiarity, more ability to have "eyes on" the property, probably more connections, etc.). I also have to agree with @Mikael Winkler with regards to how much you can learn when you're in the thick of it, so starting off with a local property can help immeasurably with building knowledge and confidence. Plus, I expect Columbus to continue appreciating above the national average but I would also expect nearby towns like Lancaster, Delaware, Marysville to benefit from that trend.
Unfortunately, I know nothing of the Raleigh market other than hearsay (which has all been positive about its prospects). People do succeed in investing out of state, but I imagine it takes a lot of work on the front end building your team and establishing necessary trust. Probably easier said than done. On the other hand, if you need a kick in the butt and something to push you to retire in the location of your dreams, maybe purchasing a property out that way might help to motivate you. Otherwise, I believe starting local and seeing where that takes you probably makes the most sense. When you do eventually move to NC, you'll still have your portfolio of income properties and have learned everything you need to know to make them still work for you from afar.