And, I'm learning from the City-Data forum that there are a lot of really seedy areas in Columbus. E.g. don't live east of Summit, or near Weinland Park. Sounds like from Short North heading west is the best bet.
I live east of Summit. Actually even farther, I live east of 4th. My part of the street (E. 13th Ave.) actually backs right up to the Ohio State Expo Center (where Equine Affaire s held).
I've never been "scared" here. There's nothing wrong with east of Summit as long as you aren't too far south. Like, I would NOT live east of Summit if I were lined up with the Short North--i.e. Chittenden Ave., 11th Ave., 10th Ave., 9th Ave., etc. 13th is probably as far east as I'd go-there's still a TON of college students out this way-like there's mostly college students on my part of the street. If you go even further north, like 15th, 16th, 17th, etc., you're totally fine east of Summit. Not to mention that the college bus system has a route that goes from central campus, all the way to the Short North, then goes from E. 11th Ave. and N. 4th St. all the way up to Hudson St. and then goes all the way back down that way via Summit St. and back to central campus. So that is a super convenient and safe way to travel, especially because you can transfer buses on campus and get on one that will drop you off at Ag Campus, which is where the vet school is located.
Most of the time people won't bother you, especially if you're smart about it. I very very rarely walk home alone at night, in fact I rarely walk around at night at all. Keep your house and car locked, always be aware of your surroundings, don't "act" like a victim, that sort of thing. I've never had a problem, and neither has my roommate who engages in decidedly more risky behaviors than I do. That being said, there ARE areas (such as the intersection of 8th Ave. and N. 4th St.) where I would probably never walk, even in broad daylight. THOSE are the more seedy areas, not the areas where there are an abundance of college kids.
However, the areas you mentioned are really nice. West of High is a pretty nice place to live, that's around Victorian Village and there are some beautiful houses there. If you're east of High, the closer you are to High Street the more expensive it's going to be. Also, the more rowdy college kids you'll encounter and the louder it will be on party nights. I like where I live because it's quiet, but it's not too far to go to a party if I want.
I'm not sure how easy of a time you'll have finding a single family home around here...A lot of the houses have 4+ (often up to 6 or 7) bedrooms and are meant for several college students to live in them. Is there a reason you don't want an apartment or a townhouse? There are some REALLY nice ones around here. My apartment is a 2 bedroom, 1 bath and I live here with my girlfriend, our roommate, and our dog quite comfortably, so it isn't terribly small. And it's nice, remodeled within the last two years. And cheap. Cherie and I may or may not be moving into our own apartment closer to High Street if I get accepted.
If you really have your heart set on a single-family house, you might want to look more towards the surrounding neighborhoods like Clintonville. It's close to campus but I'd recommend you have a car because the campus buses don't go over there and it's a pretty good hike by foot. Again though, I'd be glad to show you around when you come down.
Sorry for the novel, hoped that helped a little.