There are 2 options
- Stay at one of the hotels at Universal Studios, the Sheraton or Hilton
- Stay somewhere on the Red Line Underground Metro.
Universal Studios and Staples Center are both on the Red Line Underground Metro
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The Red Line starts at Union Station, goes through Downtown LA where Staples Center is, then up to Hollywood and onto Universal City where Universal Studios is.
The nearest Red Line Metro Station to Staples Center is 7th Street. Staples Center is about a 10 minutes walk down Figeroa Street.
It really depends on budget but there are some nice hotels near Staples Center / 7th Street area of Downtown LA. Some suggestions would be
- Intercontinental Los Angeles Downtown
- Sheraton Grand Los Angeles
- The Westin Bonaventure Hotel and Suites Los Angeles
Adventures by Disney use Lowes Hotel in Hollywood which is just behind Hollywood and Highland Mall / Chinese Theater / Hollywood Boulevard Metro station.
The easiest way to use public transport in LA is to get a TAP card. This is a plastic travel card around the same size as a credit card. You can get one at the self service ticket kiosks in any Metro station. I usually put pay as you go / Stored Money on my Tap card. You can use it on buses and the underground. As the name says you TAP on either as you board a bus or at the metro underground turnstiles and the standard fare is then taken. You dont need to TAP off when you exit, as its just one fare, no matter the distance.