Street of Silk: King's Landing Limit 1 per deck. After you play Street of Silk, choose and discard one of your locations from play (cannot be saved) Marshalling: Kneel Street of Silk to lower the cost of the next unique character your play this phase by 2.

The Red Keep: King's Landing No attachments. If The Red Keep would leave play,it goes into Shadows instead of going to its owner's hand,deck,discard,or dead pile.

If I put a Street of Silk into play and target my The Red Keep, does The Red Keepgo into shadows and I get to keep the Street of Silk in play without targeting another location?

That is correct. You target the Red Keep and it gets discarded, but its replacement effect stops it from going to the discard pile. It instead replaces the moribund:discard with moribund:shadows

Out of curiosity, what would be the counterargument that Streek of Silk's effect somehow over-rides The Red Keep's effect, sending it to the discard pile?

Or was it a question that since the replacement effect kicks in and sends TRK to Shadows, you haven't actually discarded a location as insructed to by Street of Silk? If that's the case, keep two things in mind:

1. Discarding the location is an effect - specifically a passive effect initiated by playing Street of Silk. You cannot save the location, but you could cancel the effect if you had an appropriate cancel for a non-triggered location ability. So it's not like successfully sending a location to the discard pile is a requirement or cost to successfully play Street of Silk. Even if TRK's replacement effect made the discard effect resolve unsuccessfuly (which it doesn't), there is nothing requiring the discard effect to be successful in order to keep Street of Silk in play.
2. As hinted at in #1, the use of the word "instead" in TRK makes its "goes to Shadows" effect a replacement effect. In this case, it replaces the usual outcome of "discarding" the location (ie, putting the card in the discard pile) with the outcome of putting the card into Shadows. When a card is removed from play and a replacement effect only changes the out-of-play destination, the card is considered to have been removed from play by the original effect. This can be seen in the FAQ where it describes non-character cards, killed while acting as characters, being sent to the discard pile instead of the dead pile - but still allowing you to Respond to a character being killed, not to a character (or a non-character, for that matter) being discarded from play. So even though TRK goes to Shadows "instead" of the discard pile when it is discarded by Street of Silk, the game still considers it to have been discarded - since that is the effect that actually made it leave play.