Fountain Square is very conveniently located in Downtown Cincinnati. It is crowded, especially on weekends, but they have ample parking (which does cost money) and you can also walk here if you are staying in a local downtown hotel. Once you get there, first stop and take a quick look at the Tyler Davidson Fountain- it's quite pretty and is right outside in the center of the square so you can throw some coins in and make a wish on your way to the shops. The square itself is quite a nice place to be outside when its warm out- its well landscaped and has nice gardens and sort of feels like a nice square where people come to gather.
There are plenty of things to do here besides admire the gardens and the fountains. If you are there in the winter you can go to the ice rink- this is a fairly large size (not huge but very nice) outdoor ice skating rink where you can skate around for hours (or until you get tired). You can rent skates for a reasonable fee and they have a good selection of sizes. It's not the prettiest ice skating rink I've ever seen but it does have some nice trees and you can see the square from the rink which is fun (although this also means people can see you falling down).
You can do a little shopping at Probasco market as well. This is not like chain shops or anything like that- it has cute little boutiques and cafes and has a vaguely European kind of feeling as you stroll down the street.
There is also the water wall- which is exactly what it sounds like- basically a wall of water. This is fun for kids, but gets boring after about 10 minutes; and probably isn't too exciting for adults at all.
There are also stages here that have various plays and things going on, so check the calendar before you come and see if there is anything going on that you want to see. These are often geared towards children as well. The best thing about Fountain Square though is the restaurants. There are many different restaurants along this area- ranging from inexpensive to mid-priced cafes to expensive fancy restaurants with fine dining. There is for sure something here to satisfy everyone, and you can have a nice view of the square and the fountain while you eat from a lot of these places. Its a great place to people-watch and enjoy a nice meal.