Hi, I am not clear on what you are trying to accomplish. You want to save an Illustrator file without pixels? If so then Illustrator is absolutely the right program to use so you're headed in the right direction.
Illustrator is a vector graphics program and doesn't use pixels but rather mathematical paths to form what you create. If you save as a JPG, GIF, PNG or other raster file type then your file will be made up of the pixel grid as that is how raster files are created.
If you're wanting to save a file as vector that someone can open with a program other than Illustrator, you can save as a PDF. To do that in Illustrator you go: File Menu Dropdown > Choose "Save As" > Format Dropdown select "Adobe PDF" > For options be sure "Preserve Illustrator Editing Capabilities" is checked and you can leave all of the other setting alone. You will have a vector file that can be viewed and used by other vector programs.
If this is not what you are trying to accomplish please provide more information about what you are trying to do and I will do my best to help.