Yes, the city is hilly, but there are routes you can take that will reduce your climbing. Best to pick up an SF bike map, which is probably available in any area bike shop. With regard to the weather, yep, it gets foggy, but generally only in the spring/summer, when you can get relentless fog for weeks. Fall and winter get a lot of clear, sunny days as long as it is not raining. At this moment, it is mostly sunny here. As Western Flyer indicated, bike theft is a significant problem in SF. Bring a good lock, keep an eye on your bike, and/or bring it inside with you whenever you can. Since it's a folder, that shouldn't be too much of a problem.
Most tourists stay in the Union Square area downtown because there are lots of hotels and shopping, and there is easy access to public transportation. However, it is pretty crowded/noisy/chaotic down there, so it's an area I personally avoid. If that is your thing, then go for it. Otherwise, I would recommend Cole Valley. There is the
Stanyan Park Hotel down there
(map). I've never stayed there, and it gets
mixed reviews on Yelp (for what that's worth), but the location is great. It's right on the edge of Golden Gate Park, with lots of really good biking opportunities, such as through the park to some great museums, or out to Ocean Beach, or to the Golden Gate Bridge on into Marin County (a must for the bike tourist). Lots of restaurants and shops nearby in Cole Valley and The Haight, including at least two bike shops within a block or two. Downtown can be accessed by bike via
The Wiggle or by public transportation via the N Judah Streetcar. Be aware that this hotel is near a GG park entrance where some grungy Haight St characters hang out. This doesn't bother me personally, and it's nowhere near as bad as the truly sketchy parts of the city (The Tenderloin, Bayview/Hunter's Point). I really even hesitate to mention it, since I think it is so minor, and you'd see the same sort of thing in the Union Square area anyway, but I'm just trying to give an honest assessment here. At any rate, you'll be past them in a few seconds on your bike. The rest of the park and the area in general is very nice.