Will you need to rent a car in Boulder? Maybe, maybe not. Boulder is blessed with an excellent public transportation system. In town fares are $2.25/$1.10 if you are 65 or older. Exact change is required.
If you're planning to do sight seeing in town or if you're planning to go to Denver, this is a really good way to do it. Here's a Boulder City map. Print it out at home and bring it with you.
Within a block of the Millennium, there are two routes which will get you close to the Pearl Street Mall. The Hop and the Jump.
The Hop has two routes, clockwise and counterclockwise. They cover the same territory. The counterclockwise stop is closest, just south of the Folsom/Arapahoe intersection. The clockwise stop is directly across Folsom at the end of the Millennium west driveway. Here's the Hop weekday, Saturday and Sunday/Holiday schedules.
The westbound Jump goes to the Transit Center. The eastbound Jump will bring you back along Arapahoe to the stop closest to the Millennium, just east of Folsom. Here's the Jump weekday, Saturday and Sunday/Holiday schedules.
Buses to Denver leave from the 14th Street Transit Center. The fare is $5.00 each way. There are a lot of choices and some buses are quicker than others. Here is the BX/BMX schedule.
The BX/BMX bus will leave you at Union Station near 16th Street. There is a free mall bus that goes to Broadway near the Capitol Building. The Denver Art Museum, Library and History Colorado Center are about a 10 minute walk. Coor's Field is not far from Union Station. They offer tours of the stadium.
Don't want to carry a bus map around? Google Maps has a great service. Zoom in on a bus stop, tap the stop and it will give you the next three scheduled buses by route. Plan to be a little early. Boulder buses run pretty close to schedule.
For an eye-popping ride up Boulder Canyon, take the N bus to Nederland from the 14th St. Transit Center. It's about a 40 minutes ride on a coach type bus. You can walk around this hippie mountain town, have lunch, take a ride on the carousel or turn around and take the next bus back. The fare is $4.00/$2.00 each way. Here's the schedule.
Don't want to wait for a bus? Join Boulder B-cycle. There is an $8.00 24 hour membership or a $20 weekly membership. As long as your trip is 30 minutes or less, there is no additional charge. So you can pick up a bike near the Millennium, ride the Boulder Creek Path to where you want to go, put the bike in another rack. When you want to go back, pick up another bike and go. Additional charges are $3.00 per half hour but if you switch bikes every 30 minutes, no additional charge. See here for details.