His selection of other suitable things to mount was impressive, thought maybe not as crafty as this story.
However, We (that being the royal we) are in a unique position to help! A dwarf of compulsory robust stature and with a fine selection of riding things (both airborne and not so much), I can provide a sample selection of screenshots.
So here we go.
Be warned - there might be an image or two in this post.
Let us start on the ground. The most obvious selection (and recommended quite frequently in his comments already) is the fine motorcycle. Why, I even recommended it myself, not too long ago. So please, do yourself a favour and join the dwarven motorcycle gang. Added bonus: The sidecar has a map, and I gear stories about Tamarind also getting lost in straight corridors.
Number two on the list - I could recommend the Deathcharger. Yes, you might have to run Stratholme once or twice (or so), but it is a dead horse. You could beat it, you could ride it - and it should allow you to sneer at it being dead already, so it won't talk back.
Of course, for the horde inclined former elf, there is always the raptor. However, it does have a few rather annoying disadvantages. Tickely feathers, strange troll armour and last but not least - it's basically a used car deal.
Ground based there is still one excellent option however. Better looking than the goat, with nicely shaped horns that allow a full view of the landscape in front of yourself (and the horns match the shoulder armour of plate-wearers ... maybe not an advantage for a sissy robe-wearer) and comes in a variety of colours.
The lovely Talbuk. On sale from your friendly Kurenai (and Halaa dealers).
You didn't want bears, horses or mammoths (even though the armoured horses look reasonably good and you could always spotweld the plated feet to the side of the horse), so we're already finished with the ground bound suggestions.
Which leaves taking to the air.
Preferrably a bit more elegantly and safely than her.
Although... no .. let's not go there.
Again you got a few very viable suggestions, but let me just start with ... erm... the not-so-great.
Repeat after me. A hippogryph is for treehuggers, not for stout dwarves. Nothing more needs to be said.
The colour does not matter.
The same can be said for any drake variant. I know you are the proud owner of a black one, but no matter the colour (again) they can not be trusted. Just to make sure you are aware of the eyesores drakes cause, I took a picture of the albino one - an especially foul example.
Slightly more useful are the netherdrakes - as long as you are very careful with your colour selection. Stay away from the veridian one - baby poo is not a good colour choice.
Also mentioned were proto drakes. A good selection available - some of them harder to get than others. On the ground you'll again be force into to "I'm about to fall off" position, but in mid-air they look surprisingly sturdy. And match the shoulders. Displayed below - the red one, because I don't have any of the really nice Ulduar ones.
You also mentioned liking the dragonhawk. Of course, the dedicated stable-keeper does not have to worry - there is an option available for you. Just collect a hundred silly mounts and you'll be able to ride your very own shiny blue dragonhawk.
And it's quite a feat.
It's just ....
Oh look for yourself.
Look, I know what you are thinking, but however elegant they look when a nice bloodelven NPC rides past on them, they make me sea-sick and they are not especially fierce. Mouth-froth-tentacles notwithstanding.
Even the Nether Rays look
better fiercer than this.
Can you not see yourself on top of this, brandishing a wand and a
fireball lol-smite, running down your enemies with froth dribbling from your mouth and the fangs of your flying fish?
Hmm. Okay.. point taken.
Last option then. And it's not one I recommend lightly. Have you any idea how difficult it was to drop Blacksmithing, pick up Tailoring, craft a carpet and relearn Blacksmithing just so you could see what this looks like?
Right. A carpet actually get's my full seal of approval. It looks like surfing. And that, of course, goes well with the motorbike.
So theres your options. Now be a good dwarf and choose the bike and the carpet. You know you want to.