The oval is crowded during the day but gets quiet in the evening and is pretty nice.
The Four Seasons (technically in East Palo Alto) if you can afford it and like sleek, modern properties. All hotels in and around PA are overpriced in my opinion, because there's just not enough supply to meet demand. It's often the case that the Four Seasons isn't that much more expensive than the Westin or Sheraton, and it's far nicer.
The Garden Court is also very nice; although showing its age, it has charm and character. I think they're doing some renovation. Its main advantage is location in the heart of downtown Palo Alto, within walking distance of just about everything.
Meeting other engineers in Silicon Valley is easy; it's meeting everyone else that can be hard. So if you're the kind of person who wants to leave the industry out of your social life you may have to work a little harder to meet a diverse group of people.
It depends on your interests of course, but here are a few thing I can think of:
- Concerts. You may have to commute up to SF for this one, but there are a number of great venues populated by young, interesting people. See What are the best musical venues in San Francisco?
- Book discussion groups. You can find these at your local library or search for local Facebook/Google Groups.
- Community activity groups. If you have any background in team sports, band/orchestra, or choir, you can usually find a community group for that activity. Joining a biking/running group can also be a good way to meet people (and get exercise).
- Hobby-related meetups. These can be tricky to find, but you'd be surprised what's out there. Board games, crafting, film, kite-flying, archery, robotics… whatever you're into, there's probably a meetup for it. If not, start one!
The mayor is currently Sid Espinosa as of January, 2011. 
Patrick Burt was the mayor prior to Espinosa.
Michael's and Gelato Classico both taste really good. Michael's probably has slightly better ambiance and sometimes has more selection.
Where is the best ice cream in Palo Alto?
What is the best place to get frozen yogurt in downtown Palo Alto?
See also Which restaurants stay open the latest in Palo Alto?
Jack in the Box on El Camino is open 24 hours.
If you have a car, you can also go to In N Out in Mountain View which is open until 1am (1:30am on Friday and Saturday nights) or McDonald's (open 24 hours.)
As an alternative, the Safeway supermarket in Menlo Park (off El Camino) isn't far from Palo Alto and has sandwiches and other deli stuff sometimes in addition to groceries.
Palo Alto is a city and has a mayor and a city council.
More information here:
Also, from Wikipedia:
"Palo Alto was incorporated in 1894, and in 1909 created, by municipal charter, a local government consisting of a fifteen-member City Council, with responsibilities for various governmental functions delegated to appointed committees. In 1950, the City adopted a Council-manager government. Several appointed committees continue to advise the City Council on specialized issues, such as land use planning, utilities, and libraries, but these committees no longer have direct authority over City staff. Today, the City Council has only nine members."
Expensive, but the café at the Cantor Arts center is fantastic: http://museum.stanford.edu/visit…
Per the Bike Share website, Bike Connection offers some rentals, too.
For $200, you could also get a pretty decent used bike, use it for 3 months, and at the end give it away, donate, or sell it. Try Good Karma Bikes or San Jose Bike Clinic in San Jose, or see if Bicycle Exchange in Mountain View has bikes for sale. All should be accessible by transit from Palo Alto.
Either way, don’t forget lights, lock, and helmet.
My wife and I use Delores W. Eberhart, DDS
She's awesome and very good. I referred Rakesh Agrawal to her and I think he was fairly pleased with the suggestion.