what is your age range?
my initial thought was definitely german village, but that might be a little "slow" for you if you want constant action. that being said, it seems a little sleepy but there are lots of great bars and restaurants in german village, but i think because there really isn't a central part of GV, you don't get that "happening" vibe like you do with the Short North. I don't think GV is particularly safe, though. I lived there for 6 months when I was younger and everyone's cars were constantly getting broken into - i mean, daily. I finally just started leaving the doors unlocked. I worked down there for years and I was always amazed by how much crime there was because it seems so quiet and charming.
Short North is about the same, crime wise. cars are always getting broken into. If you want a vibrant neighborhood where there's always something to do, the short north might be up your alley.
and then, there's the indie capital of Columbus, SoHud!! (aka "old North Columbus" or "North Campus" I live here, it's just north of downtown. Not too close to 70 but it's under 6 minutes on the freeway (71). housing is inexpensive and it's pretty young and diverse. It's also very safe - 2 car windows have been broken that I know of in the past 6 years (on my block). and my car was broken into, but they used a slim jim to pick the lock (how nice of them, right?) One thing I like about this neighborhood is that it really isn't a destination, so we have really great bars that aren't full of packs of douchebags coming in from the suburbs or wherever they live. Bars and restaurants in this part of town are almost all small and independent and best of all, cheap!! it's very working class/student driven. Plus you can get a lot of space and offstreet parking for you rent money, something you rarely find in German Village or the Short North.