Croatia is a beautiful country and I highly suggest you go. As far as places to stay, I don't know exactly how much traveling you'll be doing inside the country, and though this isn't answering your question and probobly deterring you from your original thought, I would highly suggest you not stay at a hotel chain.

The Croatians are very sweet, welcoming people and many, many of them offer their homes and rooms in apartments for you to "rent" (many will rent for only a day or so if that's all you want) and will do all the hospitable things that make the experience even richer. Many will show you around their city, make you food and clean your room, etc, etc. There are so many websites online that offer reviews and talk about the services; take a look around at some of those. That and they're far cheaper than hotels, as you expressed some concerns over prices.

As far as avoiding London, that's easy. I suggest flying through VIE or FRA, though FRA has many more US/Intl connections. Both airports are relatively easy to navigate and usually ontime. DBV has a few connections to both (I think 2 or so) each day too! The airport you connect through depends on the airline you want to fly ex-USA; if you want to fly a US-based airline, FRA would probably be the best option: United has a few, as does Delta and to a lesser extent Continental, American and US-Scareways. Lufthansa has many US-bound flights from FRA (including Detriot, Denver (right?), and West Coast cities) and Singapore Airlines offers, in my opinion, the best Europe-USA flight from FRA-JFK.

Enjoy!