There are hotels closer to the stadium (Like Courtyard by Marriott) but the Rams stay in either the Grand Hyatt on Pine or Hyatt on Olive. They are about a 25 minute walk from Stadium but its cool to see the players pregame walking around the hotel.

The hotels closer to the stadium save you about 15 minutes but I always stay in one of the Hyatts so I can get to see the players milling about.