First, I agree with every bit of advice given above. We are experienced road Trippers, and none of us would exceed 600 miles driving in one day. That is straight driving with stops only for fuel, food and short rest breaks - no sightseeing at all.
That said, you should limit your mileage to around 300 or less per day. Scenic roads are usually a lot slower to drive than divided highways and they have more to see and do along them. With only a week to complete the trip, I advise that you stick to the sights in the Rockies. within 100 miles of Denver you have Rocky Mountain National Park, Mount Evans (the highest paved road in the continental US), Pikes Peak, and about a dozen state parks. In fact, there are more scenic drives around Denver than anywhere else in the country. Just get a Colorado map and look for those dotted lines along the roads.
Most interstate highways are built parallel to another road. A good example is I-40, which parallels old Route 66 from California to Oklahoma City, where I-44 then takes up the parallel route. So, going from Denver to Mount Evans, you can drive US40, the parallel road to I-70, or my preference is to take I-70 to Exit 252 and then drive down US74 to CO103, which is very scenic. It takes you right to Echo Lake, the starting point for the Mount Evans road. And, in case it hasn't yet been mentioned, buy yourself a National Parks "America the Beautiful" pass at the first national park you visit. It costs $80, but will pay for itself after the first three parks.