Muir Woods is a good one. Also if you dig hiking and end up more south bay for some other reason then the Castle Rock State park is a very pretty hike. Fort Funston is also nice/easy/pretty hiking along the coast.
Ano Nuevo park along the coast south of half moon bay is good to see Elephant seals. Peer 39 in SF is touristy, but probably worth seeing the seals there.
When in SF, if you want to visit a beach then Ocean Beach is great - make sure to check out the 1900's arcade behind the Cliffhouse resturant. Also there is a romantic Camera Obscura ;-)
If you visit golden gate park - do it on Sunday when most of the park is closed to cars. In the GG park they have the Steinheart aquarium - which I prefer to even to the Monterey Aquarium.
If you two wanna try paragliding along the SF coastline (like hang gliding but with parawings) - send me a PM and I can put you in touch with someone.
Most tourists go to Alcatraz - but if you don't have a thing for prison history I'd recommend that you go to Angel island instead. They are right next to each other, but Angel Island is far prettier and nice hiking or cheap bike rentals. Both served by the same ferries - buy your ferry tickets in advance via the web, in April the lines to buy tickets at the terminals are HUGE.
I know your emphasis was on non city treks, but if you are doing the cable car thing: Check the map and get on the cable car a couple of blocks from the big end of the line queues.
You mention you might be proposing - if that involves a fancy dinner of some sort, my favorite 'fancy' SF restaurant is
http://www.jardiniere.com/. We go to a lot of SF restaurants and this place though pricey is _super_ tasty with a very non snooty vibe. One time we went with a friend who had a seafood allergy (on a very seafood heavy fixed menu) and the waiter said no problem and brought out the chef - she proposed a very tasty set of alternatives).
While in the city the Exploratorium is a great interactive science museum. If you want to visit art museums, I recommend the Legion of Honor museum over any of the others but YMMV. The SF zoo is also pretty good (especially if you like to see tigers up close
).
If you wanna go for an RV flight over the city/gate, send me a PM ;-).
On your drive to Montery - stop for lunch
here. It is a great burger and beer dive by a creek just off of 280.
Kevin