Are bound weapons worth the 6 or so Conjuration perks? Say at, level 25, would I be better off using a Bound Battleaxe with Mystic Binding or something like an Elven Battleaxe tempered to Exquisite?

I'm thinking of making a build that uses Bound Bow and Battleaxe but I don't want to be stuck grinding Smithing in the late game to have a decent weapon.

I'm really a quite committed non-magic-user, but in my humble and irrelevent opinion, not so much. The 'bound' weapons were alright in 'Oblivion'... you could have a few swings with them, chuck 'em on the ground, give them a bit of repair-hammering and they were yours to keep... levelled nicely as well. In 'Skyrim' however, they just vanish, and you can smith/enchant way better stuff for the effort.

You don't need all the perks to use bound bow. Even with low Conjuration, you can probably cast Bound bow if you wear a novice hood and take the atronach stone (that's exactly what I have done many times) and you can get the book in a fixed location without having to buy it which requires at lest 40 conjuration.
Since it lasts 60 sec, you usually can recover your magicka before it wears off.

Bound weapons with the mystic binding perk are the equivelent to unimproved daedric weapons in damage done.

Bound weapons are much more fun.

You need 0 conjuration perks to use bound weapons. Bound Bow without any perks is a damn good bow. Battleaxe is okay, and the sword is not that impressive.

If you take Mystic Binding, the bow becomes even more awesome. And sword and battle axe are better to pretty good.

Of course they are not as good as heavily smithed late game weapons. But bound bow is an awesome bow that you can get super early.

Let me give you some numbers. Bound Bow's with Mystic Binding base damage is 24 + 24. When your archery is 100, its damage is 36 + 24. With all 5 damage perks, 72 + 24. You can boost it up with enchanting to 144 + 24. With reasonable alchemy 288 + 24. Perhaps this is good enough for you. No smithing. No weight.

Or perhaps not. A real daedric bow base damage is 19 + arrow. A tricked out enchanted daedric bow can do around 50 + arrow + enchantments (50 to 160). Then with 100 skill 75 + arrow + enchantments. You can get around 300 damage with fortify marksman enchantments and 600 damage by adding fortify marksman potion.

The bow is but the battleaxe and sword aren't.

I might go for the bow until I get my Smithing up, then switch to either a Dwarven bow or an Elven bow. (Haven't decided if I want Heavy or Light armor for this build yet)

A bound bow is like an exquisite Deadric bow (24 damage) plus you get 100 free Daedric arrows - much better.