No, you can actually walk 2 blocks to that hotel. It very close.
Walking distance
Metro Link is a train you take to get to LA that only runs to Union Station. From Union Station you can transfer to Metro. You can use Google maps to plan your metro ride from wherever you are.
MetroLink terminus is at Union Station. From Union Station take either the Metro Red line or Purple line three stops to the 7th St/Metro Center station. (Pershing Square station is also close to the hotel, but there is a very steep hill, and if you're pulling or carrying luggage it'll be rough. From Metro Center it's level enough to roller skate)
Check with internet.
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