I can not personally recommend a website to find what you are looking for due to the fact I create my own, I will suggest using more precise terms when attempting a search query. If you are looking for buttons, icons, and other such things. Using these terms will allow you to better sort through the vast amount of images. Don't forget to use the term 'Vector' in place of clip art. When developing sites I prefer PNG formats and vectors for the loss-less re-sizing ability.
There are plenty of companies out there that have sites that do offer great images for websites, be prepared to fork over some cash for licensing. If you are not part of communities like Adobe's Stock Adobe I would suggest that as a next step if you are not prepare to create your own designs.