True dragons frequently have a 60 ft land speed. They can be commanded by a character with the appropriate domain on account of their having elemental subtypes (I.e. Water, fire, earth, air). Some Very Young dragons and all Wyrmlings have 8 or less HD. I mention these because 60' is very fast-- besides the option presented below, I think there isn't anything in the 65'-75' range, though I expect to be wrong about that with the addition of sufficiently exotic material. Dragons can be made undead via becoming either regular old skeletons or, for evil dragons, Dracoliches. While Dracoliches are usually older dragons, the template can be applied regardless of age category and doesn't strip elemental subtypes. This means an evil water cleric, for example, could command a wyrmling black dracolich both via Water domain rebuking and via regular old Undead rebuking.
Tiny wheeled animated objects have a land speed of 80, and less than 8 HD. Making them undead, however, is gonna be hard (or, at least, harder than most creatures). The easiest way is probably to get/build a wheeled thingy with a skeleton, animate it a permanent animated object, then apply the Skeleton template to it. But that, obviously, would be a pretty weird animated object, and the GM may well rule that, while it has bones in it, the construct doesn't "have a skeletal structure" for the purposes of the template. 80' is an untied best for base land speeds (8HD or under), though.
Between the Tiny Animated Object (with wheels, mind you) and the super-common 60 ft move speed are almost no creatures. There are larger (and consequently slower) wheeled Animated Objects, two epic creatures (the Devastation Beetle and Thorciasid, but if you are okay with level-draining epic creatures you should skip ahead to the Weirder Stuff section below), and a single 12 HD creature from Monster Manual II: the Rukarazyll. It's an Outsider with the Earth Subtype and a 70' move speed. You could cast enervation on it and ensure it loses 4 HD permanently before killing it and raising it as undead, but that's definitely cheese and the creature is pretty exotic. Beyond Animated Objects and the Rukarazyll, there's no stuff that's even remotely reasonable to allow that has a base land speed over 60 feet without even considering hit dice.
Two creature templates-- Shadow Creature (from Lords of Madness and Manual of the Planes) and Dark (from Tome of Magic)-- modify speed. It is unclear if the Shadow Creature template is acquired or inherited, but the Dark template can be either and is "a simple, streamlined version of the shadow creature template" (ToM 160). Using them both, consequently, is extremely sketchy, but if you could you'd get to add 10' to base speed and then multiply it by 1.5. Dark can apply to any creature, but Shadow can't apply to constructs but can apply to undead. If they're both allowed, your tiny animated object could theoretically be a Dark Shadow Tiny Animated Object with a base speed of 135'.
Another template, Paragon Creature, gives massive bonuses to everything, including tripling a creature's base speed. Additionally, it does not increase a creature's Hit Dice. A Paragon tiny wheeled animated object skeleton has a base land speed of 240'. A Paragon Wyrmling Black Dragon Dracolich has a base land speed of 180'. The Paragon Creature template is in the SRD and the Epic Level Handbook; whether or not that counts as 'exotic' is debatable, but certainly the template is game-breakingly problematic in terms of player-controlled creatures, which are often limited by HD. If it is allowed and Shadow Creature is also allowed, you possibly bypass the multiplication nerfing rule if Speed is close enough to distance to be concrete. If not, the total multiplication is 3.5 rather than 4.5.
Level drain can lower a creature's HD. A legendary horse can be made into a legendary horse skeleton, and also possesses an 80' base speed. Unfortunately, it also has 18 hit dice, so you will need to give the horse skeleton 10 negative levels to fit it in the haunt. It's not easy to give negative levels to undead, but it is possible-- a holy weapon, for example, grants one negative level while wielded, while an intelligent item can grant up to 3 negative levels (or more if epic rules are in play) per item just by being carried. 4 30-ego good-aligned intelligent items should be sufficient to fit a legendary horse skeleton into a haunt. Templates can apply here as well, obviously.
Branching into epic, the Elder Titan possesses the highest base speed of any creature, at a whopping 150'. A small mountain of 62 separate intelligent items (or less if they have higher egos) should reduce a Paragon Elder Titan Skeleton's 70 HD to 8, allowing you to haunt shift it. You can command a Paragon Elder Titan Skeleton by being a level 140 evil cleric, or by lowering its Hit Dice first (by convincing it to pick up your super holy sack o' items, I guess) and being a more reasonable level. In any case, the 450' move speed appears to be the fastest base speed in the game from creature+template, although if you can add the Dark and Shadow templates as well this increases to either 560 or 720 feet depending on how your DM views Speed for the purposes of the multiplication nerf.
There are feats that increase one's speed: for example, Epic Speed. Your target creature could have some of those, particularly if it's a slightly more exotic non-mindless kind of undead (like a Bone Creature, for example). Epic Speed is notable because dragons can take Epic feats pre-epic for some reason.
The Speed Enhancement+5 ability from Weapons of Legacy's Menu A grants, as a supernatural ability, a 5' enhancement bonus to a specific speed mode, which could be land speed. The Speed Enhancement+10 ability from Menu B of the same book does the same thing but 10'. These are not temporary bonuses. The Monster of Legacy template (ibid) can grant an undead of 5-8 HD, among other creatures, the effect of an option from menu A. At 6 HD they could instead have a Menu B option. The two don't stack, so this is a 10' increase at max. Since these are supernatural abilities, Manipulate Form (see below) can optionally be used instead of the template to give these abilities to whatever base creature you are using.
The Manipulate Form ability of the Sarrukh from Serpent Kingdoms can, because of the existence of the Incarnum Speed supernatural ability of the Duskling Barbarian substitution levels in Magic of Incarnum grant additional speed to a creature, dependent on that creature's ability to invest essentia in it. There's basically no way that this doesn't count as 'exotic', so I'm not going to bother discussing it further.