Keep to browsing simple sites, in simple browsers and the modern web is still "accessible" to your iMac G3. You definitely need more RAM, and an SSD will also help, as the Short Timer said. I won't bother you with frogfind or 68k.news as they've been already mentioned.
news:
text.npr.org
lite.cnn.com
hckrnews.com
guardian.gyford.com/
www.cbc.ca/lite/news?sort=trending
reddit:
teddit.net
old.reddit.com
weather:
wttr.in
search:
duckduckgo.com/lite
Retrozilla and ArcticFox PPC (both by Wicknix, available on this site or on his, just google them) are much better choices than TTFx or InterwebPPC for your aged hardware. I am shocked at how much browsing I can still do (admittedly on a fast G4, not a G3) with Retrozilla. At times I forget I am on such an old computer!
Dronecatcher can still stream youtube on a 500 mhz imac G3 using all of his methods-I won't bother detailing them, again, search this forum if you are interested for his posts on the topic. This is his youtube video from three months ago:
Links2 is a text based browser (will display inline images, sometimes) that will actually feel FAST on your iMac. Ported by alex_free, its available on the forum, just search for it. Many many websites will "work" though you have to get used to the fact that everything is justified LEFT, and there is no javascript. At all. That also gets you around many paywalls like nytimes.com and washingtonpost.com and theatlantic.com
Stream internet radio with Fstream, or with one of the macintosh garden's hacked itunes versions.
Don't give up yet! Change your expectations a little. If you wanna get super creative you can VNC into a modern computer (even like a Raspberry Pi) and "run" a modern browser inside your ancient mac. Yes, it's cheating, but it also blows people's minds, which is always fun.