Any Dwarf inn. I would pick the Kharanos inn if I had to pick one.
I spent a lot of time in Thelsamar and actually had my hearthstone set there for a year, because I was on my old, shitty PC back in those days and had to avoid major cities. 256MB of RAM, a 1GHz P3, and onboard graphics running Windows XP and playing WoW. It's a wonder that even fucking worked at all.
Silvermoon inns, the one on the west side the most. Blood Elf inns are always my first choice, feels comfy and relaxing, it's really magical!
Thinking the usefulness, Shrine of the Two Moons is best choice. Especially I like to bind my HS to the balcony. I felt very empty when I rolled an ally char to find out there's no balcony innkeeper on Shrine of Seven Stars...
Whatever that Alliance inn was called in Dalaran. I had an angsty 'I wish Blood Elves were still with the Alliance' moment back in WotLK, and would always look towards that inn that I could never enter with yearning.
The only time I ever got to be inside that wonderful place was during the Quel'delar questline. It was glorious. ;~;