We LOVE swimming. There are tons of places with indoor swimming here, not sure what's available in columbus. We especially love it in the winter because we feel all 'sneaky' that it's so cold outside and we are in the warm pool!!!!!! They also have hotels with indoor water parks here that you can buy a day pass for.
We also like to play mini-golf and laser tag (neither as fun for the 3 mo old!!!! but you could 'wear her' and still play) and both usually have some indoor facilities open during the winter.
Also, the museums here will offer family 'classes' on the weekends - learn to sew, or make a clay pot etc that you can do as a family. It's usually pretty cheap - we did one at the Children's museum and it was like $3 and we each made a bag.
One additional thing that we used to do when we lived in another city was volunteer at a food bank at our church (but there are TONS of them). My daughter was 3 at the time and it was a GREAT experience for use to do together. We went one Sat morning each month from 8-12. The first hour and 1/2 we helped organize the bags and then you handed them out the rest of the time. We did it here with our church for a while, but have sorta stopped and now that I am typing this realize we should get back to doing that!!!!!!!
Have fun :-)