Are you really talking about ACR? And are you talking about raw files? You don't want to resize raw files. But you can use the Image Processor in Photoshop to create copies of your images, and you can specify the size that you want when you set up that dialoge.
just for the records: the only Adobe App I know of that allows to control the output file size is Fireworks, where you can define the expected target output filesize (eg. 100kB) and FW will do its best to reduce image quality as much as necessary in order to make the final JPEG fit into this boundary. It doesn't support batch processing, however ;-)
Adobe Apps are for a good reason primarily focussed and designed to preserve image quality as much as possible. Squeezing pixel into a spcified range of bytes can't do that and will always sacrifice quality.
As you said, the "File Save" feature (lower left button) in ACR only supports image quality, where "low" will likely give you the smallest possible filesize for a particular image, but also the "ugliest", by means of introducing compression artifacts.
You may now either reduce the image dimensions via the crop tool or scale them down using the export settings link below the main window. Simply put, the fewer pixels, the smaller the output file, as compression will only get you so far. You won't get, let's say a 50k JPEG from a 14 megapixel RGB image, but you might get close to that byte number from a 1000x800 px image. It may look crappy, but here you have your output file size
If you're on Windows, the only tools I found to create nice looking "small file size" JPEGs in batches is RIOT (Radical Image Optimization Tool)
http://luci.criosweb.ro/riot/download/ Available as a stand-alone tool with side-by-side comparision preview, or as an export plugin for various file viewers (IrfanView, XnView etc.)
It can handle many image formats including DNG, but it'll ignore any ACR development settings!
So I'd recommend to export TIFF files from within ACR to avoid compression artifacts even in "hig quality" jpgs and then batch process those TIFFs with RIOT to optionally scale and compress those intermediate TIFF files to your heart's content. It's scaling methods are IMHO also superior to the plain vanilla "bicubic" method found in PS or ACR.
In order to squeeze some extra 20-30k from the generated files you can strip off the XMP and EXIF data and the preview thumbnail.
Hope this helps.