I haven't done it personally, and I personally wouldn't bother, but if you're determined to do it, check out these pages:
http://lowendmac.com/2016/cpu-upgrade-options-for-mid-2007-imacs/
http://lowendmac.com/2018/penryn-t9300-9500-cpu-upgrades-for-the-2007-imac/
Your best options are the Core 2 Duo T9300 or T9500 (with 800 MHz bus speed and 6 MB cache). The T9500 is a bit faster than the T9300 but costs twice as much. But then again, it's still only about $40 total, so not a big deal. They will still be slow machines, maybe half as fast as a fanless MacBook Core m3, but they would be significantly faster than a 2.0 GHz Core 2 Duo. It would make for a noticeable improvement in surfing speed.
I have a Core 2 Duo 2.0 and a Core 2 Duo 2.26 (both with 1066 MHz bus speed and 3 MB cache) and the 2.26 is actually noticeably faster, despite having only a 13% improvement in clock speed. It makes a difference for some web pages and for watching videos. Even though the h.264 is hardware accelerated on both those machines, the extra CPU speed means less dropped frames and glitchiness. I suspect it'd be even better with a 2.6 GHz T9500.
Also, if you upgrade to T9500, you can install 10.13 High Sierra on it. High Sierra runs well as long as you have at least 4 GB RAM and SSD. It's bad with a laptop hard drive, but with a desktop hard drive, it can be tolerable as a secondary machine.
EDIT:
Hmmm... That machine has a Radeon HD 2600 Pro. AFAIK, that does NOT support hardware h.264 acceleration. If true, then that's a downer. Surfing without hardware h.264 acceleration is that much more sluggish when viewing a webpage with video on it.
