The downtown arts district (around 6th and Vine near the Aronoff Center), and Upper Main St in Over-the-Rhine, are two prime entertainment areas. Three of the good eating places in the former neighborhood are Jeff Ruby's Steakhouse, La Normandie, and the five-star French restaurant Maisonette. Main St draws a younger crowd with its trendy eating places, bars, and small clubs. Two more memorable dining establishments downtown are Izzy Kadetz's deli, and the one-of-a-kind Italian joint Scotti's at 919 Vine.
Downtown Cincinnati is easily walkable, with small city blocks. Streets running north are numbered starting at the river, with even-numbered addresses on the east side. Here's the way old-school Cincinnatians remember the order of the north-south streets downtown:
Chops (Central Ave.)
East-west streets start with 3rd, and go numerically up to 9th (with part of 8th also known as Garfield Place.) In place of a 10th St, there's Court St. 11th St doesn't exist, then Central Parkway runs in between 12th and 13th. Even-numbered addresses are on the north side of the street. Vine St is where crosstown streets change from West to East.
You'll find spirited differences of opinion over where the "best" places to go within a mile of the river on either side of it are.