Yap is a bit more expensive than most of the places I travel, but still doable for around $100 per day or so. It could be done for less with no diving, but that just seems like an unreasonable thing to give up after having made it all the way to Micronesia.
Accommodation was, I found, the biggest and least flexible cost. The cheapest thing I could find in Colonia was $50 per night, and there are surprisingly few good camping spots around the main islands. Food costs are pretty flexible, but to commit to a full diet of self-catering is to inflict oneself with a curse of Spam and Canned ham and processed fish that nobody should have to live with. If you’re going to try it, look for a good meal on the cheap and filling lunch menus (especially at the Marina Grill… perhaps the most consistently delicious food I had, with lunch specials around $5).
Oh, and for diving, stick with the guys at Beyond the Reef. They were cheaper by about $20 for two dives/ day, and seemed like the most fun to hang out with for the day anyways.