Cincinnati Subway
Between 1920 and 1925 the City of Cincinnati spent six million dollars building a subway system, which was supposed to ease congestion and spur growth in Cincinnati. However, when funding ran out in 1925, the construction came to an end with nearly seven miles of the subway dug or graded, but no track laid. Several attempts to complete the subway have been made, but all proposals have ultimately failed. However, sections of the tunnel have been used for various purposes including the conversion of the Liberty Street station into a nuclear fallout shelter. The money borrowed to build in the twenties was finally paid off in 1966.
By car
For getting quickly and conveniently to most places in Cincinnati, you will need a car. Be aware that there is a street grid only in Downtown and its surrounding neighborhoods. Outside of those parts of the city navigation can be tough, with street names changing constantly, and unintuitive routes being the norm. Particularly tough, is getting up to Mt. Adams, where if you don't go down the right series of one way streets you could end up getting flung out to one of its surrounding neighborhoods or Eden Park. There are a few signs directing drivers to the neighborhood, but they are easily missed. A good roadmap or GPS system is highly recommended if you plan on driving around.
Many roads are very narrow and very hilly reflecting the age of most of Cincinnati, which was built well before the automobile was the mainstay of transportation. Some streets will feel like country roads with the occasional urban house/apartment built where the terrain can support it. Other roads such as the aptly named Straight Street quite literally go straight down a hill at a very steep grade. Be careful when driving in inclement weather and remember that when parking on a steep slope, point your tires towards if downhill or away if uphill from the curb and use your emergency brake.
I-75 is to be avoided around rush hours at all costs. While traffic isn't as heavy as one would encounter in much larger cities its still quite formidable. The large amount of truck traffic combined short ramps and many blind corners create a traffic nightmare. If you can, take the much less traveled though still somewhat congested I-71 which is most easily accessed by taking the Norwood Lateral OH 562 across to it at Norwood.
Parking is generally cheap and plentiful in Cincinnati. The few trouble spots are around the University in the Clifton/CUF/Corryville areas Uptown, Downtown, and Mt. Adams. When parking in Mt. Adams, be aware of parking restrictions by reading the signs, there are far more of them than you'd encounter anywhere else in the city, due to the narrow streets and dense population of that neighborhood.
On foot
Some of the older neighborhoods in Cincinnati are quite walkable, with the Clifton Gaslight District Ludlow, Over-The-Rhine, Mt. Adams, and Downtown being amongst the easiest to travel by foot. Due to massive depopulation of what were formally neighborhoods with densities approaching that of New York City, like Over-The-Rhine and the West End, Cincinnati is way more car oriented these days with most destinations being too spread out to walk to. However, many of these districts were built to pedestrian scale and are worth a stroll so long as one exercises caution see the stay safe section. A visitor from a larger East Coast city may expect neighborhoods of similar scale and architectural composition to be filled with people, but instead oftentimes they are full of abandonment and the problems that come along with it. However, places like Mt. Adams, Downtown, or Clifton around the Gaslight District don't have these problems are well worth exploring by foot, park your car outside of the neighborhood and walk right in.