Hey ladyjny,
First let me welcome you to the KY forum. Before I answer your question, I'll throw a couple of facts out there:
Covington is a city in Kenton County, Kentucky, United States. As of the 2000 census, the city population was 43,370; it is the fifth-most-populous city in Kentucky. The racial makeup of the city was 87.05% White, 10.14% African American, 0.24% Native American, 0.34% Asian, 0.03% Pacific Islander, 0.63% from other races, and 1.57% from two or more races. Hispanic or Latino of any race were 1.38% of the population. According to recent Census estimates, Northern Kentucky is one of the fastest growing regions of the state (granted, I feel it is a bit skewed...for example add 100 people to a city of 24,000 and then add 100 to a city of 595,000...which is going to appear to be growing faster percentage wise?).
Anyway, on to answering your question. I have never lived in Covington (or the surrounding areas like Newport), but I did live relatively close and frequented the NKY/Cincy area quite a bit. Over the last 15 years, it has changed a lot. Overall, I'd say the overall vibe I get from covington/newport is a trendy/growing urban suburb (if that makes sense). The reason I call it an urban/suburb is simply because Cincinnati is right across the river and a lot of people travel there to work...so it is similiar to a suburb. However, it is still urban (being that it is next to a large cities and for all intensive purposes is right next to Cincinnati instead of out on the fringes). Here is a view from covington into Cincy (well, actually Newport but you get the idea):
Now, I don't know what your political beliefs are, or whether you lived in a diverse section of New York, but Covington (and Cincinnati on the whole) will be very different from that sort of environment. Even without looking at the demographic section above, I can tell you that most of NKY is white, middle class republican (yeah, there are some minorities, but I am going with the general feel). In addition, Cincinnati I'd said is a very conservative city (remember when they kicked the Hustler store out of downtown because it was inappropriate?). I'm not saying this is a bad or a good thing (personally I like Covington...right next to Cincy, pretty close to everything like the Reds, Bengals, malls, etc), but it will probably lack the diversity you are use to seeing in NYC.
I also think covington feels like a smaller community (granted it is pretty small at 24,000). The fact that cincinnati is right next door helps to relieve this a lot (especially if you like larger communities/cities like me), but at times, it can feel like smallville, KY. That is just my personal opinion and I am sure others have differing views on this.
One thing you may want to check out while in NKY is the Newport aquarium/Newport on the Levee (I am assuming you know the region...if you don't, Newport and Covington are saddled right next to each other....the only reason they are seperate is because there is a small river between them). Also have the Reds, Bengals, and several shopping spots very close by and Labor Day fireworks are always fun. Hope my ramblings helped a bit.
This is a website with a slideshow from around covington (I think it'll point out why sometimes the city seems urban and why sometimes it feels like it is small).
http://gallery.kyhometown.com/slideshow.php?set_albumName=covington (broken link)