I would advise looking into rentals in the Worthington School District. Most of these rentals are new condos or apartment buildings or homes. They are located, mostly, in the city of Columbus in Worthington schools. The ones in NE Columbus are located very close to the popular Polaris Fashion Place.
Worthington and New Albany both have swim teams and pools on the school's campuses. Thomas Worthington had a great swim team when I lived in Worthington a few years back. Also, Worthington Schools/Columbus City Limits NE areas (whew!) are located very close to Westerville. Many work at the Polaris area of Westerville and live or have children in Worthington schools.
The neighborhoods I am thinking of are N. High St, just north or south of I270 (many highend rentals.) Anything near the Crosswoods Development (near the previous recommendation.)
The neighborhoods would be off of Sancus Blvd, Lazelle Rd, Park Rd., and the Polaris Fashion Place.
Here is a GOOGLE LINK to the area:
http://maps.google.com/maps?hl=en&q=...-8&sa=N&tab=wl This would a perfect place for a Columbus newcomer to stay, get use to the city, be in a suburban school, highway access to OSU or downtown on 71, 315, and 270 to other Columbus 'burbs and Easton, a large metro park (Sharon Woods) and right next to Polaris Fashion Place.
Also, Worthington city limits may have some homes for rent. Worthington City Limits begin SOUTH of 1270 and High St.