@Craig Smith - hey! I was in your spot before...
I'm going to offer an alternative perspective, and it's this: stick to your backyard. Here are four reasons why.
1. It's less risky. If you invest OOS, you open yourself up to a huge risk - finding a great PM and making sure they do a good job. My first building was a 33-unit Class C, and I was often at my building multiple times a week. Granted, I was self-managing, but when I had a PM and was OOS, the building rapidly deteriorated. Sure, you could just find a really good PM, but that's hard (and, also really hard when you don't live in the city you invest in because finding a good PM takes a lot of networking, and you can't do that easily being OOS).
2. You develop deep market knowledge. Good, long-term thinking real estate investors recognize the value of market knowledge. Being in your backyard and driving by your property, you get an unparalleled view at the neighborhoods on a truly block-by-block basis. I have a building where two blocks west is horrible, and two blocks south are nice, single family homes. But I wouldn't know if I wasn't there all the time. And knowledge is power.
3. You develop a foundation for scale. Good investors recognize that successful scaling requires specialization. Unless you plan to stay in Ohio forever, it's invaluable to have your entire team, market knowledge, and portfolio in one place. Now, large companies diversify out, but that's once they reach thousands of units. Just google up larger real estate companies and you'll find that most of them specialize in a few types of real estate (geography, class, strategy, etc.). The big boys generally don't hop around from place to place based on perceived appreciation trends.
4. It's easier to network. How are you supposed to network with people and talk to them about the nuances of Ohio if you live in NY? I live in Chicago, and there are A LOT of nuances to Chicago that OOS people won't know about until they get here. Which is fine. It gives me a competitive edge against them!
My main point is to think long-term. I know it seems tempting to look elsewhere because of the relatively lower prices, but remember to think long-term - think about the market knowledge, scale, network, and power of having your portfolio consolidated in one place. Of course, my advice varies depending on your investment goals and the type of building you're looking to buy (ex. NOT wanting to scale, getting a single tenant triple net property, or getting a Class A property are all *possibly* exceptions). That said, I truly believe it'll help you far more in the long-term staying in NY than saving a few bucks in the short-term by investing OOS.