The Gateway Marriott does indeed have a tunnel that goes underground which connects the hotel to the Crystal City underground, which is quite close to the actual Metro.

The Westin just "opened" as it was the Sheraton before. You do have to go outside to get to the Metro but you can cross 18th to the Marriott and go that way or walk directly to the escalators just east of Rt. 1 (note Rt 1 is actually elevated here so you don't actually have to cross it).

One thing to keep in mind, there's not a ton of breakfast options in that area, with mostly the hotels the only places offering it.