Here are three to check out, all close to each other in the Clintonville neighborhood north of downtown and the OSU campus area:
The Train Station (
www.trainstationohio.com), located on Indianola Avenue. Exclusively trains with a good selection of rolling stock and engines in HO scale. Also N, Z, G, and Lionel.
Robbies Hobbies (
http://www.robbies-hobbies.com), located on North High Street. Eclectic selection of new and used materials in HO, N, Z, G, Lionel, American Flyer along with slot cars, toys, etc. If you're looking for something specific, they probably won't have it. If you go with an open mind and don't mind shopping in a garage sale environment, you can have a lot of fun.
Hobbyland (
http://www.hobbylandstores.com), located in the Graceland Shopping Center on North High Street. General purpose hobby shop with a good selection of trains and lots of scratchbuilding supplies.
All three stores have friendly helpful staff. In addition, a busy NS/CSX line parallels Indianola and runs right behind the Train Station. A local group of foamers can often be found hanging out at the Cooke Road crossing.
Also, not too much further away, in Worthington, is the Ohio Railway Museum (
http://dev.ohiorailwaymuseum.net/) which offers trolley rides (at least they used to, it's been a while since I visited).
Have fun!