My best advice is to take a look at a book first or the Croatia website (see below) - it's not clear what your (exact) interests are or if you have a good sense of the geography or what's doable. Focus on only one region to minimize travel time (in other words, don't try to go to cover places that are way too spread out geographically in only one week). Croatia is not very easy to get to or inexpensive from the US. All flight connections will involve some stopover. I found Split to be a good base but that's because I was really interested in seeing some islands (Brac, Korcula, etc) that were very accessible from there (and for me, Croatia was a side trip from Bosnia). Split itself was interesting in its own right. In your case, pick either north, south or middle - the country is very long from south to north. Everyone will likely nominate Dubrovnik as a "must see" - it's lovely and unique, but extremely touristy and more expensive than other parts of Croatia...there are plenty of local, less touristy spots. Even if you skip it, there will be plenty of other jaw dropping places to see (the coast and islands are an obvious highlight, but there are also beautiful natural parks and wonders like Krka, Plitvice Lakes, and Mljet)
You can find some trip ideas here:
http://www.croatia.hr/
I think it's very useful to think in terms of "regions" for your short trip (go to "Explore Croatia"):
http://www.croatia.hr/en-GB/Journey-through-Croatia/Useful-information
Once you have a rough itinerary, post again and you'll get much better, more fine-tuned advice. Best of luck! Croatia is a dreamy location and you'll have fun planning.