Maybe try Dinah's Hotel and Garden in Palo Alto for the hotel - the price seems to be right, and the area is good and close to Los Altos. Check Trip Advisor, though - I've never stayed there.
And I would definitely get a car. Distances are long here in Silicon Valley, and public transit is too time consuming for a quick trip. If you can, try flying in and out of San Jose (SJC), which is about the same distance as SFO to where you want to be. I think a shuttle (or train) is going to be required to rent a car at either airport, and I cannot speak to which is more convenient. I would not bother with Oakland, as it is very inconvenient to this area. Southwest Airlines will get you to Houston if you don't mind giving up the miles, and serves what may be a more convenient airport in Houston (HOU vs. IAH) - which you choose depends on your destination within Houston.
I would also recommend checking out Beltramo's wine and liquor store in Menlo Park. They have one of the largest selections of very well priced wines I have ever seen - including a very large selection of Montrachets, which I do not often see in such large quantities.