Where is the best place to park in Downtown Cincinnati?

I prefer the Fountain Square Garage, especially if you're attending an event on the Square. You can take an elevator from the garage that lets you out on Fountain Square. They have self-pay machines that take cash or credit cards. They have flat $5 weekend and evening rates... $10 for Bengals games... and it's convenient to everything.

One of the best parking garages I have used downtown is on Race Street close to 3rd Street and its called Rays. Its an older building that was converted into a garage and its really reasonable compared to other lots and their proximity to downtown hotspots. The rate is now $6 for all day and its about a 5 min walk from the stadiums and ballparks and Fountain Square. The owner is super friendly and always has someone at the entrance to greet you when you pull in. If you become a regular he will probably get to know you on a first name basis.

Since street parking is consistently monitored by police for overdue meters, I'd say parking lots are your best bet if you're planning on staying in the neighborhood longer than two hours. Sure, you'll have to pay, but not nearly as much as you would in many other cities. During major local events such as Reds or Bengals games, parking rates naturally increase steeply the closer you get to the ballpark/stadium. Otherwise, though, parking rates are pretty reasonable. A couple bucks will get you several hours in many places. My favorite place to park downtown is at Music Hall.
They just opened a newly renovated parking lot open 24-hrs to the public. It's clean, safe, and very central. During performances, admission to the garage is a flat rate of $8 (event parking, essentially). I'm not sure what the standard rate is otherwise, however.