It really depends on what you're looking for in a neighborhood; however, I would probably recommend Over-the-Rhine as a good location. Over-the-Rhine is seeing a resurgence in popularity and has had much new housing added, as well as restaurants, shops, and other businesses. It would be a good location for a young couple (especially without kids). If you work in or near Downtown Cincinnati, it is a perfect location, as well. A young couple would do well in this area, because there are a lot of other young people living here, plus Over-the-Rhine features a vibrant nightlife scene. There are a variety of properties both for rent and for sale in this area.
Besides Over-the-Rhine, another renewing neighborhood might be a good location, such as Northside. Northside has a lot of trendy places to eat and a decent nightlife scene, plus some industrial buildings are being renovated into housing. Home prices in Northside are also pretty reasonable. Northside is a hip area that is a popular place for the GLBT community, as well as younger people. It is relatively convenient in location and has a good small community feel.
Another neighborhood that would be good for a younger couple is Oakley. Oakley is not as expensive as nearby Hyde Park, but has many of the same amenities and convenience. Since Oakley is right next door to Hyde Park, you can easily head to all the popular Hyde Park places, but without paying the higher housing prices of Hyde Park.
Pleasant Ridge is another neighborhood great for a younger couple, especially if you're looking to purchase a home. I know a number of young couples who have purchased their first home in Pleasant Ridge. Pleasant Ridge has a convenient central location, tree lined streets, and a walkable business district. Housing prices in Pleasant Ridge are very affordable, making it a great neighborhood for a first time home purchase.