Cardinal Hotel I think it's fair to say that most of us visiting Stanford now stay at the Cardinal. Warning: it has two types of room - those with en-suite facilities and those without (down the corridor). Be careful you know which you are booking. IMHO the continental breakfast (charged extra: obtained by token, at a café underneath) isn't worth the money - better to walk a few doors further to Coupa Cafe, walk onto University and find a coffee shop there or wait till you get to campus. Coffee in the lobby is free. The Cardinal is less than 10 minutes walk from the bus station (for the Stanford shuttle) and the Caltrain station. RG http://www.cardinalhotel.com/
Airbnb, various locations Many people in the area use Airbnb to stay in private residences. Some travelers to Palo Alto from the Hydra community have been very satisfied; your mileage may vary.
Even when renting an entire home or apartment, I've found Airbnb can often be the most cost effective option in Palo Alto, and there are great options not too far off of University Ave. This is particularly true if you're traveling with colleagues and don't mind sharing an apartment with 1-3 other people. – MM
Hotel Keen This "bijou" hotel is owned by the Cardinal. Its opening offers made it attractive but now that the offers have gone it is expensive for what it is. Very small (bijou) rooms which are fine if all you want to do is sleep in them. To sit and work or read, I find them a bit claustrophobic. OK breakfast included. 5 minutes from the bus and Caltrain stations. RG
Stanford Inn, 115 El Camino Real, Menlo Park (Not to be confused with the Stanford Motor Inn.) Both Matt and I have stayed here a couple of times but gave up on it. Yes, it is cheap but the whole place has a slightly tired, run-down air and too many things don't quite work as they should. It's not a bad place, and if everything else in the $100-$150 range was booked up I'd go back. But it wouldn't be my first choice. Best part of 15 minutes from bus and Caltrain but handy for the Stanford shopping mall. No breakfast provided but there are sources in the mall. RG Tom adds: This is probably the lowest overall cost. It's a block further north than the Best Western. It's really a bargain though some may say you get what you pay for. http://www.stanfordinnusa.com/
The Zen Hotel, 4164 El Camino Real 2.9 miles from the library. While this is a bus ride away, it was very comfortable, recently remodeled, spacious (large room with desk and couch, nice linens), not too expensive and clean. Breakfast was included and offered good variety. I had a car so the distance was not an issue. http://www.thezenhotel.com/
Stanford Terrace Inn is in a great location, and a nice, non-chain hotel at the southern border of campus. www.stanfordterraceinn.com
The only drawback is that it's not close to downtown, where most evening activities have been held. Otherwise nice amenities and service. Decent, if not full-featured, breakfast offerings. --David C-S
The Schwab Residential Center has guest rooms These are located in the Graduate School of Business, and somewhat convenient to both central campus and downtown Palo Alto. The nightly room rate as of Feb 2016 is $140 single occupancy. Please note: Due to summer Executive Programs, availability may be limited (or nil) over summer. http://www.gsb.stanford.edu/facilities/accommodations/guest_rooms
Both Lyft and Uber operate at SFO–and are about $40 to the Stanford area. Pickup is fast and the drive is direct. Get the app for your phone and order. Taxis from the airport to Stanford-area should be about $80-$90. There is also a train (possible until about midnight, $10, but takes a transfer to Caltrain at Millbrae) http://www.bart.gov/guide/airport/index.aspx, and Super Shuttle: http://www.supershuttle.com/ (~$30)
Also consider Socialdrv (http://socialdrv.com/): An shared ride service specializing in airports. You can reserve online ahead, and the drive will track your arrival. It's pretty awesome.
There's also a SamTrans express bus (route KX) that runs roughly hourly between the airport and Palo Alto transit center (the bus/train station referred to above): fare $2.00 (03/2013). Takes just less than an hour. http://www.samtrans.com/schedulesandmaps/timetables.html Sadly, this very useful route no longer runs. (2015)
Downtown Palo Alto is a pleasant 20-30 min walk from Lathrop Library. The Palo Alto Caltrain station is between downtown PA and campus; it's a 15-25 minute walk to Lathrop (or take the free Marguerite shuttle).