Here we go again with another young professional threat, your lucky though because im a recent graduate living among singles so I have some advice...!!!
The areas of central columbus are really the best for single/young/higher energy living (yet still laidback) These areas are all in central city Columbus (close to childrens), and are nice gentrified urban neighborhoods. If you lived in any of these places you wouldn't need to get on a highway to get to work.
Really my favorite urban/nice neighborhoods of columbus are the ones just north of downtown. Victorian village/and italian village are both great. Victorian village has a really nice urban park that is surrounded by all of the homes and some rental properties, but mostly condos these days. I feel much more safe in a lot of columbus nice central city neigborhoods, than in some that lie 2 miles or more from downtown and have become fiilled with low incomes and immigrants etc...
www.shortnorth.org
is a good site that details the commerical strip which lies north of downtown and both victorian village and italian village lie next to. There are some great apartments right on High St. in the short north itself too.
The Short North general area is your best bet for walkable community with nearby restaurants (although many are more highend), bars, some boutiques, and lots of coffe shops.
German Village is almost walking distance to Childrens and lies just south of downtown. It is a very quaint beautiful setting. The area is not really young single central though, some younger couples live there, and these days mostly older well off home owners. However, the Brewery District is just west of german village, and the Brewery District has a lot of rentals. Two brand new apartment buildings there are Brewers Yard (has an outdoor pool) and Liberity Place. I would look into both if you don't mind being south of downtown.
Also, Grandview Heights area is just west of the Short North and would be an easy enough commute, but a few minutes further than the other areas i Have mentioned. Grandview Heights is nice and has a mix of home owners and many young professionals and singles.
Downtown (the arena district) has some high end apartments in the Arena Crossing. They have a website, you can see the apartments on the Arena District website, i would just google it. There's a nearby market, and this is also right near the Short North.
I would look into personal adds to see if any condos are being rented. This would be a good bet since urban columbus has seen a lot of condo development recently.
If your thinking you want more of a suburban neigborhood with singles the NW section of Columbus has some options and many condos and apartments. Also it seems that some singles have settled around Easton Town Center. Most of those apartments are complexes, and you would be near the best shopping in columbus, but not in a walkable city setting.