If you want to see what's happening around your favorite major US airport, check out Flightaware. It and several other sites track flights with IFR flight plans (which covers most of what operates at SFO). You do miss VFR traffic (the guy in the Piper Cub going to Marina, for instance) and military/most government flights. Few helicopters show up, either, because they rarely file a flight plan for local operations. But the non-military loud stuff usually does show up. Information is typically delayed 15-20 minutes, but if you note the time of a particularly loud flight you can look it up a few minutes later if you want to file a complaint.

Flights have a symbol (big jet for widebodies, small jet, and straight-wings for prop jobs) and a tag that shows:

flight or airplane registration number - aircraft type
altitude (feet above sea level) - speed (knots)
origin - destination - time

Click on the symbol for more information.

Based on my experience (not in the Bay Area), the worst noise is from landing traffic, not takeoff. Closer to the ground, and adjusting power more radically and often plus flaps, landing gear etc. OTOH, SC is far enough away from SFO that even the landing traffic usually runs at 5-7K ft. altitude or more so while noticeable it shouldn't be loud (SC Mtns ridge is at about 2K feet along Summit Rd., with a few higher peaks, so at worst the planes are 3K ft. or more above ground level). Where I live I'm about 15 miles off the end of the runway at a local UPS cargo hub - not horrible, but quite a few wide-bodies at maybe 2K AGL for landing in the early morning (0300-0600) and also late afternoon-evening. Military appears mid-morning & early afternoon - now THEY'RE noisy (the sound of freedom)!

Here's SFO: [flightaware.com]
You can enter other airports in the search box. Those affecting the Santa Cruz area might include (but are not limited to - there are some other general aviation airports around):

San Jose: KSJC | Oakland: KOAK
Hayward: KHWD | Watsonville: KWVI
Palo Alto: KPAO | San Carlos: KSQL (lots of small jets & turboprops at these airports)
Moffett Federal: KNUQ (though it shows little traffic - military and many government flights don't show up)
Monterey: KMRY | Salinas: KSNS

Now what does this have to do with trains? Are trains equally noisy? Probably seem to be, up close, and being on the ground you can be closer. But trains run much less often in most areas than planes do around the Bay Area (or most other major airports). In SC, I suspect that even with RTC's little dream cars you wouldn't get much noise in the dead of night.

Bikes? What kind (hate Harley v. Ninja races up the freeway at 0200 - disturbing even 2-3 miles away)? Pedal bicycles are quiet but their riders frequently aren't. Oh well, if you really want quiet go build an anechoic chamber to live in ...