Save for Web allows you to choose JPG as one of the output formats, so I'd suggest trying that again and looking for a "format" option or "file type", etc. Irfanview is one option, XnView is another (my preference). In XnView you can get great results without too large file by doing the following:
File->Export
Go to JPG tab (if not already there)
Quality to 90 or 95 if necessary
Change DCT method to "Float (best but slowest)"
Smoothing factor 0
Subsampling factor to "1x1, 1x1, 1x1 (best quality)"
Progressive enabled (you don't have to use progressive, it won't really affect quality, but can make slightly smaller file size on large images)
Optimize Huffman table enabled
Click the magnifying glass in the middle of the two preview images above to get to 100% view, then click and drag around on either of the image previews to pan around the image and see if there are any compression artifacts. The compressed version is on the right, the original on the left.
- Oshyan