Here in the Dayton, Ohio, area a chain called Jersey Mike's (www.jerseymikes.com) has sprung up in a few locations. Ditto for already-mentioned Quizno's. There has been a local chain called Super Subby's (www.subbys.com), but I went there once and thought it was way too greasy.
There's also a Columbus-based chain called W. G. Grinders (www.wggrinders.com), but I find the food slightly too salty. Penn Station (www.penn-station.com), based in Cincinnati, is full of grease like Subby's IMHO.
When in the upper Midwest I tend to go to a Wisconsin-based chain called Cousin's Subs. Their website is www.cousinssubs.com
if you're interested! (They also have locations in Arizona, Colorado, California, and Texas, having expanded outside of their home turf!) The closest one to Dayton is in Indianapolis.
As for Subway, I have not eaten there since March 1998. I remember going to one sometime before then and getting a pizza sub that was cold.
I just thought I'd mention I have been to McDonald's hundreds of times but have never visited White Castle!