Is it possible to manage without cash, but with credit cards only when visiting San Francisco?

Yes. Absolutely. Almost all that you mention and tips can be paid using credit cards in almost all of the USA. SFO is a major metro and I cannot think of any establishment which will not happily take your money in the credit card format. It helps to keep a few bucks in cash and the only areas that I think you will require cash for are :

1. Alms : If you love giving alms or handing out change to panhandlers, then you will obviously need to have some cash on hand.
2. Street vendors & performers : Street performances (musicians, mimes, artists), will obviously only accept cash as tips, and many street-side stands (selling arts and crafts, or snacks) will only accept cash. These are not extremely common in the U.S., but they do exist in certain areas--including San Francisco.
3. Grocery store purchases less than $10 : If you end up shopping in ethnic grocery stores or mom & pop stores, a lot of them will not accept credit cards for bills lesser than 10 bucks (primarily because of the transaction fees they end up paying)
4. Rain check tickets : One of the things I do when visiting tourist attractions in major cities is, subtly, ask some merchandise vendor near by if he is selling rain check tickets. If you are able to strike 'that' chord, those people will only sell such tickets for cash.
5. Gentleman's services : Getting a dance on a card can be very cumbersome and I have rarely seen anyone get a lap dance on a credit card. But the club will jolly well give you cash out on your credit card. So you can get cash from the club itself.
6. Vending machines : If you want to buy newspapers, sodas, snacks, etc, from the local vending machine, that will generally take loose change only.
7. Mugged : If you venture out into the dangerous areas and unfortunately get mugged then there are chances that you will probably end up relatively more injured for not carrying any cash.
8. Laundry : There are a few unmanned laundry places which will only take quarters. So you gotta be prepared for that.
9. Buses : Most buses require an exact fare in coins. However, you can charge a prepaid Clipper Card with a credit card.
10. Toll roads and bridges : In some areas these are set up for credit card payments (Oklahoma turnpike will take a credit card payment, if memory serves), but many will require either cash or a pre-paid account of some sort (not practical for most visitors).

Toll booths will usually have different queues for drivers with cash/credit cards in the USA. Going by this link it looks like you will be good with a credit card in SFO.

This may be wrong about the toll roads and I stand corrected. Please see https://travel.stackexchange.com/a/20828/4584 for the correction

As a correction to HappyBuddha's answer, the San Francisco Bay Area has many toll bridges, and they do not accept credit cards at the toll booth.

The main alternative to cash on the toll bridges is FasTrak, an electronic tolling system. You buy a transponder (grocery stores often sell them) and link it to your credit card. If you rent a car, it will probably already have a transponder; the tolls will be charged to the rental company, who will tack on a surcharge and collect them from you.

On the Golden Gate Bridge (but not the other bridges in the area), there are no cash tolls either; anyone without FasTrak will have their license plate scanned and receive a bill at the address where the car is registered.

I'd also like to point out that, while most restaurants, stores and bars accept credit cards, in my experience there is a significant minority that remain cash-only. This particularly includes little hole-in-the-wall establishments, which IMHO offer some of the best food in the City. So if you refuse to use any cash, you may miss out on those.

The only thing I can think of is MUNI buses and streetcars, which only accept cash or Clipper. Even MUNI passes from the drugstore can only be purchased with cash. However, getting a Clipper card will save you a lot of time if you're riding transit a lot, as you can board at the rear door of the bus or streetcar instead of having to wait in line at the front. Also, if you plan to ride the ferries (highly recommended, even for a round trip to nowhere), the discount for Clipper is significant.

Otherwise, I know more than one person who visits "the City" routinely and does not carry cash. Even the types of small businesses that one might expect only take cash often take cards, thanks in no small part to the little iPhone/iPad payment devices. [Full disclosure: I have friends who work at one of those companies.] Not to say that every hot dog stand takes cards, but many do. Also, apparently Coit Tower is cash-only, as is the Musée Mecanique. Even vending machines often take cards now.

Let's try to list the common places where you need to spend money:

• Taxis: accept credit cards.
• Restaurants/fast food: accept credit cards.
• Groceries/supermarkets: accept credit cards.
• Hotels: accept credit cards.
• Car rentals: accept credit cards.
• Movie theaters: accept credit cards.
• Famous shopping stores: most accept credit cards (some don't, like sam's club).
• Gas: Credit card accepted.
• Museums: not sure they will accept credit cards.
• Clinics: credit cards accepted.

These were the places you most likely to visit.

Most of the above are from personal experiences.