The Blue Moon isn't a hotel ( just to point out lol ) it's a pub which is located in Varrock, just north of the Small Bank.
Varrock, near the southern entrance.
the blue moon inn for the shield of arrav quest is in varrock... go to the town square and head south to a pub... that is the inn
he is in varrock in the blue moon inn. that's the bar closest bar to the entrance by the heroes guild.
in the blue moon in at varrock, by the dark wizards and sword shop its got a beer icon
In Varrock, Just south of the general store. Look for the pub symbol on the mini-map.
The blue moon inn is near the wilderness. You can attack lvl 2 NPCs or a black knight.
he is in the pub in vorock by the pub closted to the mage circle
You can Propose as soon as chelsae or mark arrives, at the hotel
The Blue Moon Inn is in Varrock, southeast of the Tailer Shop. Go to Varrock Square, travel south, pass the Tailer shop and General Store. It should be the bar below the General Store. Hope this helps. =]
Half Moon Hotel was created in 1927.
The Blue Hotel was created in 1899.
You can give Straven the Intel report (assuming you killed Johnny the Beard to get it, in the blue moon inn) but using it then clicking on Straven.