Mansfield would be an ideal spot, 1 hour from Columbus, Cleveland & Arkron/Canton. But I am not aware of any facilities that can host a big volume. From what I understand, Cyclops is not what it used to be when it was privatley owned. I am not sure if anyone even plays there anymore and driving by it looks pretty run down. It was a premier 4 diamond complex years ago when men's slowpitch was thriving. Nothing else in Mansfield even comes close...Hamilton Park has 2 diamonds for mens leagues. Last time I was at Liberty Park the fields were covered with broken beer bottles. Sterkle is a beautiful 5 diamond complex but 3 of those infields have grass. Madison also has a great 4 diamond complex but 3 of those infields are grass.
Ontario hosts a big Rec All Star tournament the last weekend in July. 24 teams play on 5 fields, but that is split between 2 different parks.
Ashland Brookside seems to be the best suited area spot with no youth tourneys. Galion's Peco Park could do it too.