Of course, you need to seek out a couple of good bike shops in your area and try out various bikes in your price range. Try some lighter flat-bar road bikes (for example something like a Trek 7.5 FX , or a Specialized Sirrus, or a Giant FCR). These hame the same mountain-style handlebar that you are used to, but less of an upright position. They are more geared towards fitness and distance riding than the bike you have.

The other option is a true road bike with the racing-style drop handlebars. Many people say they are much better for long distances. I am new to biking like you, though, and I'm really happy with my flat-bar road bike that is comparable to the ones I mentioned above. I added bar ends to give my hands some flexibility of position, and I find my bike very comfortable but speedy and athletic.

Good luck!