Tom,

1. The best clubs or schools to rent from. Airport proximity to the
city is important to me.

Depending on which side of the city you're at, San Carlos and Palo Alto
are the interesting ones to the south, Gnoss is pretty much the only
option to the north. Oakland and Hayward are on the East Bay. At San
Carlos, Diamond Aviation (?) has an interesting selection of rentals - a
lot of new and cool stuff. At KPAO, for long term membership, West
Valley Flying Club is much worth looking into.
Since we're talking Silicon Valley here, all the airports and clubs/FBOs
have nice websites, so some googling is in order.

2. Recommended instructors for an IFR rating.

If he is still in the area and in the business, Charles Harris. The man
is priceless! Tought me crosswind landings in a way that finally made me
see the light. See http://www.campbells.org/Airplanes/Diary/toc.html for
a taste.

3. What are conditions generally like for VFR flying in the Bay Area?

You have to deal with the marine fog layer often, so the IR is a really
good idea. You'll want to get mountain flying instruction, since
hot&high conditions are close.
Other than that, the scenery and the amount of options and variety of
areas in close proximity are nothing short of sensational. You can be in
the high desert in an hour or two, or in Alpine mountains, or on a
gorgous beach or in a picturesque village or in a spectacular city.
Nowhere else in the US have I found that many 100-$-burger destinations
within easy reach. And then there are the Napa and Sonoma valleys.

4. How's the city tour? I lived in NYC for a while and loved it there.

The "Bay Tour" needs some advice from locals on ATC procedures, but it
is real nice. A good way to do it from the southern fields is to combine
it with lunch at Napa, Santa Rosa, Sonoma or Lampson/Clear Lake.

Yes, I am writing this from Hamburg, Germany ;-)

--
Thomas Borchert (EDDH)