What does ascetic hunter do? I assume zen archery substitutes your wis modifier for your dex modifier on ranged attacks...

Ascetic Hunter allows you to freely multiclass between Ranger and Monk and stacks the levels between the two classes for purposes of determining unarmed damage and favored enemies.

What would be awesome would be a feat that allowed you to apply something like Stunning Fist through a ranged weapon. Dunno if such a thing exists though.

It seems like your flurry ability is going to be kinda up the creek (unless you expect him to get into melee combat a lot). Maybe look into some of the alternate class options (like from UA or something. I don't recall if it had anything) to replace the ability. Or, perhaps you could still have a ranged monk, but use thrown weapons like the sai and shuriken rather than a bow. Then you could still use the flurry, just at a short range (far shot would be your friend). Or combine the two--so the ranger aspect kicks in at long range (50+ feet), and then you switch to ranged throwing as the enemy closes. I really like the kind of skirmishing/hit-and-run tactic these days, so this character sound pretty cool.

I figured Flurry would come in handy so that I'm not one of those archers that's crippled outside of ranged combat.

I was really going more for an archer than just a ranged-combat Monk. Those are good ideas, though.

I don't know how useful Far Shot would be for me if I'm darting around and trying to make full use of Manyshot + Shot On the Run + the Monk's high speed.

Well I figure that Far shot would give you an extra square on your close range. I see you taking the monk's huge move speed, run up to close range, slap someone with a thrown weapon, and then run out of range again.

I think there was a feat Dash in Complete Warrior or something that improved your speed. That might help with the concept (since you'll be sacrificing levels of monk for ranger levels)

This is rather simple to do.

I play this very archetype for my prime character. He is an elven Monk, and his primary weapons are Unarmed Attack and (Elf racial prof) Longbow.

I made it abackstory of my character that his bow is nearly a religious experience into itself and he abhors melee combat with anything but his hands and feet.

There's a new feat tree in PHB2 that can grant a monk a ranged attack. Fiery Fist requires you burn a stunning fist use to gain 1d6 fire damage on any unarmed attack, but its successor Ki Blast lets you burn two uses for a ranged touch attack that deals 3d6+Wis damage. Both feats require an attack bonus of +8.

Very interesting.

If I was gonna use PHB2 feats, though, I'd wanna try out a melee Fighter just to flavor those feats.

Those are mighty spicy as well

You can't use Manyshot and Shot on the Run at the same time, in the RAW (rules as written).

Manyshot [General]
As a standard action, you may fire two arrows at a single opponent within 30 feet.

Shot On The Run [General]
When using the attack action with a ranged weapon, you can move both before and after the attack, provided that your total distance moved is not greater than your speed.

(Emphasis mine)

Attack Action is a specific action (make a single attack). Manyshot is a different standard action. They don't stack.

(Similarly, you can't Spring-attack to a Dual Strike, you can't Spring/Fly-by to a Ki Whirlwind, or any other standard action. You can only make a single attack.

In the PHB2, there is a Spring Attack progression, that lets you make multiple attacks as part of a Spring Attack. But that's the only way.