For proximity:
* Near
* Adjacent
* Nearby
* Next to
* Beside
For similarity:
* Alike
* Similar
* Resembling
* Comparable
For intimacy:
* Intimate
* Familiar
* Confidential
* Trusting
For being shut:
* Shut
* Closed
* Sealed
* Locked
For being near to a conclusion:
* Nearing
* Approaching
* Imminent
* Pending
For being tight:
* Tight
* Snug
* Secure
* Firm
For being secretive:
* Private
* Confidential
* Secret
* Hidden
Please provide more context about how you're using the word "close" so I can give you a more accurate synonym.