There are a lot of public tennis courts in San Francisco. My favorite being in Russian Hill. I don't know many hotels that actually have tennis courts, you might want to see if you can stay at a hotel that offers access to the Bay Club, but I highly doubt they have relationships with any hotels in the area. I think you'd be most happy stay in San Francisco city, rather than just the outskirts. Look at the Marriott on 4th Street. The St. Francis (westin) is a very old historical hotel. very neat. I also like the Palace, again very old school San Franciso hotel. Both are very nice and don't run down. You wouldn't be disappointed at either of those too.
As for a pool in San Francisco, if you are staying in June/July/August in San Francisco city limits it will be far too cold for an outside swim, you'll want to look for an indoor pool. If you are staying in the south or east bay, the weather can get up to 100+ degrees.
My family has always enjoyed The Marriott at Fisherman's Wharf. Plenty to do for all within walking distance, or use the trolley. Likewise, if you are wanting to go to Alcatraz, get your tickets on line and early!
Lastly, be cautious about renting a car. Driving in SF is not much fun, if you can avoid it. Think about day trips outside of the city with someone else driving. It may save you a lot of time and money. Please check with the hotel directly you select to stay with and seek their concierges recommendations.
Good luck and make sure you take some warm clothes!
The SF Marriott Marquis located south of Market at fourth and opposite the MOMA has an indoor pool on the fifth floor that is quite large. I can't tell you much about tennis in the area but a concierge can. Parking at this hotel is expensive, as are all the downtown hotels, and driving in the city can be exciting and harrowing too. There are streets where when you park you are sure your car is going to tilt over! But driving down Lombard Street is fun as long as no one is behind you and your brakes are working.
Let me second what others said about our summer weather--it is cold and foggy most of the time, and sun breaks occur around 1pm and last until 3 or 4 PM when Sundowner Winds bring that heavy fog (marine layer) along with an onshore flow from the Pacific. Take a sweater and a coat to be comfortable, even gloves and a hat. The humidity along with the temperatures in the 50s make for a chilly summer day and night.
Some of the best summer peninsula weather is a little further south (30 miles or so) in Palo Alto and Menlo Park. Both enjoy limited summer fog and abundant sunshine. Palo Alto has a Caltrain station that can whisk you into the city of SF fairly quickly. Menlo Park's train station is also good but is not as near to downtown (such as it is). If you opt for this location Marriott has a Courtyard and Residence Inn in the area with several full service hotels about 12 miles to the north (San Mateo) and south (Santa Clara) Both have outdoor pools and Santa Clara has two tennis courts. it is adjacent to the California Great America theme park, formerly a Marriott operation but now independently owned Parking is charged at both these full service hotels but at a more reasonable rate than in the city
Other hotels include one of my favorites, the Stanford Park located on El Camino Real near the Stanford Campus--a gem of a place with fairly steep prices. Elegant and secluded too with European luxury touches. Kids might find it boring of course.
With your two kids the best place is to stay at the San Francisco Marriott Fisherman's Wharf. It will provide you and the entire family a lot of options.
Also the hotel @ San Francisco Marriott Fisherman's Wharf has Alcatraz Package >> While staying in one of San Francisco's most popular destinations, the Marriott at Fisherman's Wharf, take a cruise on the Bay and experience the unforgettable Alcatraz