Programs: F9 Summit, Marriott Silver, La Quinta, Avis First
I live in downtown Denver. If you have to rent a car, I would look at just using the hotel parking. Any surface lot or garage will not give you any in/out privileges, so you are paying the higher "first hour" charges each time. Additionally, the surface lots require prepayment and it is sometimes not possible to pay for multiple days, requiring you to go back out and pay again to display another receipt on your dash. Although some parking meters in Denver now allow overnight parking, they are installing many sensors that during the daytime, check to make sure your car is moved every two hours. At the end of the day, you probably won't be able to save enough money to justify the headache.
There is a cheap parking garage at DCPA, adjacent to the convention center, but no overnight parking is possible. For the day, it's something like $5 for in by 9, out by 5:30.
I would lose the rental car and cab/shuttle into downtown instead, and for the days you'd really need a car, there is an Enterprise on site at the Hyatt and Avis/Hertz/Budget nearby (walkable) as well. If you use Avis, you can usually return at the airport for no extra charge, so you can put your sightseeing at the end of the trip. As a bonus, you can save paying the airport taxes on your car rental this way.