I checked the following areas you requested and added Hilliard in as well because it is near Dublin. The only rental that meets your criteria at this time is a nice Condo in Dublin. It is in the Tuttle Crossing area, Dubin schools, 3 bdrm, 2 full baths, a half bath, full basement, pets welcome, no section 8, 2 car attached garage side load all for $1400.00 per month.
If this sounds like something you would be interested in please let me know so that two things can get done.
1. Send you the property detail report so you can look at it, and
2. Let me know if you want me to research this further to see about negotiating better lease rate and terms that are favorable to you.
614.288.0423 or email: firstname.lastname@example.org
If schools are important to you you'll want to focus on communities such as Upper Arlington, Dublin, Powell, Lewis Center, New Albany or perhaps Gahanna. A good site for information on local schools is http://www.greatschools.org/ . Some of these areas are pricier than others (New Albany for example is one of the pricier parts of town) and you'll want to consider all of these factors before deciding on a community/neighborhood. Another factor to consider is you and your family's lifestyle and what type of amenties you'd like the community to offer, for example most of the communities referenced offer great parks and a number of fantastic golf courses as well as convenient access to shopping and entertainment but they each have their own perks, for example if your work requires that you travel frequently New Albany or Gahanna might be a bit more appealing as they offer quick access to the airport.
Both Upper Arlington and Grandview are in close proximity to the University area and would be a great choice. Dublin will be a bit of a commute. For school and neighborhood demographic information visit the websites for the school districts and the suburban areas, they can be a great resource. I'd be happy to run a residential rental search for you to locate a rental. Let me know if I can help!
Katie McCann, Realtor