There are plenty of things to do in Denver that would be great for
half-day trips and not require much travel. There are two museums within walking distance of the hotel; the Denver Art Museum
http://www.denverartmuseum.org/visit_us and the Colorado History Museum http://www.coloradohistory.org/exhibits/coloradomuseum.htm.
There is the State Capitol Building
http://www.milehighcity.com/capitol/ just a couple of blocks east of the hotel, as well as the Denver Mint
http://www.usmint.gov/mint_tours/index.cfm?flash=yes&action=StartReservation which provides tours, but unfortunately no free samples!
The Denver Zoo http://www.denverzoo.org/ and the Denver Museum of Nature and Science http://www.dmns.org/main/en/ are located very close to each other and are reachable by bus or taxi from the hotel downtown. They have an IMAX theatre at the museum.
Just 3 blocks north of the west end of the 16th Street Mall (which has a free shuttle bus that runs east and west along the mall) is the Wynkoop Brewery, where Mayor Hickenlooper got started in his first campaign for mayor http://www.wynkoop.com/history.html .
At the west end of the 16th Street Mall, the Tattered Cover Bookstore has a 3-story downtown location. What Mensan can resist books?!
http://tatteredcover.booksense.com/NASApp/store/IndexJsp;jsessionid=abc\Xakg91I1RedyQ-DKbr?s=becomeaffiliate. Their main location is on east Colfax Avenue, easily reachable by bus http://www.rtd-denver.com/ .
There are retail shops and restaurants all along the 16th Street
Pedestrian Mall, including a multi story shop and movie theatre called the Denver Pavillions http://www.denverpavilions.com/, which is only a couple of blocks away from the hotel. Some of the stores are Barnes and Noble (there are those books again!), Nike and Virgin Records. Just another couple of blocks away (west) Aveda just opened a new salon/spa/training institute http://www.avedadenver.com/aveda_guests.php .
There are downtown maps and business directories available for free at the stops along the shuttle route along the 16th Street Mall. There is a free shuttle that runs from one end of the mall to the other. The Adams Mark Hotel sits along the route of the 16th Street Mall and the free shuttle.
If you like baseball, Coors Field http://colorado.rockies.mlb.com/col/ballpark/index.jsp , home of the Colorado Rockies, is just a short walk north from the mall shuttle on 20th. Tickets can be had for as little at $4 to sit in the "Rockpile".
Further west of the city, in Morrison's foothills, Bandemere Speedway
http://www.carson-cctt.com/events/bandemere01/bandemere01.htm hosts weekend events during the summer including the Mile High Nationals.
There are summer evening concert events in Morrison at the Red Rocks natural outdoor amphitheatre http://www.redrocksonline.com/index.asp .