Moving to Dayton
"How does it compare in the outdoor recreation department?"
Honestly, it depends what you're comparing it to. I lived with a roommate from New Hampshire, and it's nothing like New England, Colorado, or California. She thought it was terrible that she couldn't climb a mountain. There aren't mountains and there isn't an ocean...it's the midwest! There ARE lots of lakes nearby, where you can boat, waterski, fish, and swim. They're lots of fun if you have a boat, and if not you can rent one. You can canoe or kayak in most of the area's rivers and lakes as well. You're within 2-5 hours of actual mountains and good rock climbing...the further you drive, the bigger the mountains get! There are tons of local parks where you can walk or hike, there are mountain bike trails, and there are indoor rock climbing places as well. In the summer, there are outdoor festivals every weekend. Dayton has a good network of long bike trails too. Additionally, those country roads outside of the city make for a great place to take long road bike rides on the weekends. There are several groups to meet up with to get started. There are also numerous adult-league sports both indoor and outdoor, year-round.
"How long of a drive to Lake Eerie(sic)?"
Parts of Lake Erie are 3+ hours away from Dayton. Other parts are much further east, and take longer to drive to. Almost the entire northern border of Ohio is Lake Erie.
"Are there any nice historical neighborhoods with good schools?"
Oakwood is both historical and has VERY good schools. Most of Dayton's historic neighborhoods are part of Dayton Public Schools, which generally are not "good". There are very good private schools within the city though, mostly Catholic. I lived in the Oregon District and absolutely loved it, but I wouldn't have lived there if I had children, because of Dayton Public and the yards being small. Oakwood is near University of Dayton and pretty close to several hospitals. It's very nice.
There is a Children's Hospital in Dayton, Miami Valley Hospital is very large, and there are several other hospitals as well, including in the suburbs. I think there's even a large group of practices called Dayton Medical Center. North of Dayton is Upper Valley Medical Center...it's a beautiful new facility in Troy.
Speaking of which, the suburbs of Troy, Tipp City, and Vandalia have good school systems and Troy and Tipp are less of a suburb and more of a small town/small city feel. They have numerous historic homes and also a traditional downtown Main Street. Those 3 are all north on I-75. South or east of the city are the more sprawling suburbs like Centerville and Beavercreek.
I liked growing up there enough that I moved back in my twenties. You'll like it as long as you keep a positive attitude and focus more on what it DOES have than on what it DOES NOT have. That was my roommate's problem, and I learned a lot from listening to her whine about the place!
For a city of its size, it has a lot of museums and historic markers. There is the USAF Museum (free), the Dayton Art Institute (free except for special exhibits), Boonshoft Museum of Discovery (natural history), and various parks centered around local history (Wright Brothers, NCR, etc.). Nights (and days) spent in the Oregon District! Fifth Street gets closed off for certain holidays. Halloween especially stands out in my mind. Costumed revelers walk the streets, listening to live bands, drinking, eating, watching freak shows, and admiring others' costumes.