I do like straw however the students who were teaching a workshop with me yesterday do not like it. We both mulch with cardboard or layers of newspaper first, then they like to lay wood chips. I prefer straw, it's easy and cheap for me.
Do you have a chipper?
Do you have compost or chopped leaves?

Mr friend got salt marsh hay last year and really liked it - it was thin, and no seeds. She just bought it at the local feed and garden store (Blue Seal) - but this is New Hampshire where this kind of stuff is pretty easily available.

I don't like using hay or straw, either. Last year, I got grass clippings from other people from the local dump. It worked ok, though I worried a bit about chemicals. I've also used my own compost.

A couple weeks ago a tree trimming service dropped off a FREE load of chipped wood and branches at my home. Here is a list of places to try calling. Don't be discouraged if it takes a few dozen calls to find free material. It took me a few weeks to find a reliable source. Now I can have dump truck loads delivered for free.

Try calling your local utility company. They are always clearing trees away from phone lines and power lines.

A lot of tree services are more than happy to drop off a load chipped wood rather than paying to drop it at the dump.

Some garbage companies land fills have a service where you can get chipped wood or leaves too.

Some cities offer free mulch from all the city and park trees they have to maintain too.

Sometimes you can find free composted manure or chipped wood on Craigslist too.

No one should ever have to pay for mulch or chipped wood. I wish I knew what I knew now years ago.

Mountain- small sawmills should have organic saw dust.
Leaves, straw, pine cones,hay,power line wood chips.
For wood chips call the power company.

Thanks all for the great leads. I should have explained that I'm wanting to mulch my actual raised veggie rows so sawdust or wood chips wouldn't work (at least I don't think I would want to use stuff that takes so long to break down, right?)

I will ask some folks who mow big lawns around here if I can have their clippings. We are rural and almost noone around here puts any chemicals on their grass.

Thanks again!

I mulch with fresh wood chips and my garden looks like the garden of eden.

You don't have to worry about the wood material tying up the nitrogen in your soil if it is just laid over the top. It only does this when mixed into the soil. If you mix it in this fall when your garden is done, it should be broken down by next spring. If you can find it, I think it's a good solution to your problem. You could also lay down newspaper, then top it with the wood, and remove the wood come fall if you feel the pieces are too large to break down over the winter.

I mulch with pine straw.