Some official sites with a considerably large collection (not all manga are free to read though):
shonenjumpplus.com
pocket.shonenmagazine.com
seiga.nicovideo.jp/manga
comic-gardo.com
mangaz.com (very old manga)
pixiv.net (mostly short manga)
If you want to read a certain manga, you can also:
1. Search for it in mangadex, in the title page, you might see a link for the "Raw" - the official digital source of the manga.
2. Search for it on google, use the original name of the manga in japanese, the publisher of the manga might have a website for reading chapters for free (though they are usually only available for a limited amount of time)
3. Stalk follow the author's twitter or pixiv if he or she has one. Nowadays lots of authors upload low quality version of new chapters there to promote their manga.