Lima has a good, not great, mall. There's also a newer, nice but expensive theater.
There used to be a place called "Squirty Worm" with go-karts and such, but I'm not sure that it's still open.
There is an adult video-store.
We used to go to Lima all the time. Now whenever we want to go out we typically go to Findlay or the other direction to Columbus.
Findlay is a nicer version of Lima. It's a bit bigger, and is growing, odd for an Ohio city. They have an ice-rink and a new theater and a mall similar in quality to Lima's.
Columbus has basically everything, but it is a larger city. We like to go to Easton, which is a sweet outdoor shopping center. They have really nice restaurants. There is Short North too, and the Arena District. We also usually go to Tuttle Crossing Mall and go to Blue Jackets games a LOT to spend evenings.
But the best thing to do in Ohio is Cedar Point. King's Island is good too. You can also do hiking and such; Ohio is more than just Kansas with people.
EDIT: You may not be able to tell by reading, but we pronounce "Lima" as "LIE-muh," not "LEE-muh." It's a thing with Ohio, butchering city names like Toledo, Versailles, Marseilles and shortening "Wapakoneta" to just "Wapak."