Which is a better style to write default return case in if-else private String GetFacilityName(String facilityHexID) {
    if (facilityHexID.equals(FACILITY_AIRCON_HEX_ID)) {
       return FACILITY_AIRCON_NAME;
    }
    else if (facilityHexID.equals(FACILITY_FAN_HEX_ID)) {
       return FACILITY_FAN_NAME;
    }

    return facilityHexID;
}


Or

private String GetFacilityName(String facilityHexID) {
    if (facilityHexID.equals(FACILITY_AIRCON_HEX_ID)) {
       return FACILITY_AIRCON_NAME;
    }
    else if (facilityHexID.equals(FACILITY_FAN_HEX_ID)) {
       return FACILITY_FAN_NAME;
    }
    else {  
       return facilityHexID;
    }
}


They essentially do the same thing. I'm thinking first one is better from the standpoint of "Write more code only if you have to" and the second one is better from readability aspect.

I'd use a switch statement with default case but I'm using a old version of JDK.. so I can't use it on Strings.

Which one is better?
I'd remove both elses:

private String getFacilityName(String facilityHexId) {
    if (FACILITY_AIRCON_HEX_ID.equals(facilityHexId)) {
       return FACILITY_AIRCON_NAME;
    }
    if (FACILITY_FAN_HEX_ID.equals(facilityHexId)) {
       return FACILITY_FAN_NAME;
    }
    return facilityHexId;
}


I think it's easier to follow. (It's called Guard Clause.)

Some other notes:


I've switched the equals to CONSTANT.equals(inputParameter). Now it handles null inputs too and does not throw NullPointerException.
I've renamed the method to camelCase. It's more common in Java to start method names with small letters.  (Code Conventions for the Java Programming Language, 9 - Naming Conventions)
I've changed ID to Id in the variable names. I prefer camelCase here too because it's usually easier to read. From Effective Java, 2nd edition, Item 56: Adhere to generally accepted naming conventions: 


  While uppercase may be more common, 
  a strong argument can made in favor of capitalizing only the first 
  letter: even if multiple acronyms occur back-to-back, you can still 
  tell where one word starts and the next word ends. 
  Which class name would you rather see, HTTPURL or HttpUrl?