Try olive oil.Was at the store today... not paying $6 for a small jar. Broke out the food processor and made some. Used lemon instead of vinegar. First attempt was pretty good, taste similar to Hellman's, but there was an 'off' flavor. Used vegetable oil, think I need to use something else next time. Wasn't thickening, had to add a lot more oil than the recipe called for to get it to thicken.
Worst part was trying to get it out of the food processor into the jar.