How long will you be in SF? From you r post I assume you will be staying with an uncle who lives in San Bruno. Whether to rent a car or not depends on what you want to do/where you want to go. San Bruno is nothing like NYC. It is a small suburban town - there is nothing to see there, and nothing to do there but sleep. Like Lumpy said, you can take BART to SF - you just have to get to the San Bruno BART station (and BART stops running around midnight, which might put a damper on late-nite activity in SF). As to BART- NB: trips to and from SF and the airport area (San Bruno) will have extreme delays on Saturdays and Sundays, requiring the use of shuttle bus in the middle of your trip, because of re-building rail tracks south of the City. You can drive in SF, it's just that parking is difficult downtown and in the most urban part of the city. But you can easily find street parking in other parts of town. Although a city, most of SF is actually residential areas of single family houses. One can get around SF on public transit - there a couple subway lines, and lots of buses - but bus travel tends to be slow if you have to change lines. If you want to go to Golden Gate Park, Lands End, or wander the Presidio, a car can come in handy - it's not necessary. If you want to go anywhere outside of the city itself, not on a BART line, a car is VERY useful - almost required.
If you are like a lot of us, you might enjoy a visit to the wine country - about 90 minutes north of SF. Skip Napa - crowded and pricey. Just as good wine without the hassle in Sonoma county and in Dry Creek Valley (NW of Healdsburg). There is an unpretentious relaxed gay scene in/near Guerneville (Sonoma County - 15 miles west of Santa Rosa). People swim in the river there - sandy beaches, clean water, no alligators or snakes, redwoods. Mostly a hamburger sort of place, but one can spend $300 on dinner there as well.
If you want to check out the gay scene, it is mostly centered around Castro and Market streets, and a couple locations "South of Market." I haven't been inside a gay bar here in years, but walking down Castro Street, one sees hundreds of gay men, any time of day or night. The annual Castro Street fair is October 2.
Other than tips on gaylife, you will find the most information (and can get any question you have answered) athttps://www.tripadvisor.com/ShowForum-g60713-i30-San_Francisco_California.html
TripAdvisor has an app for phones, but I have found it very cumbersome, and with only 5% of the information it has on the web if accessed by computer.
A lot of tourists go to Fisherman's Wharf and Pier 39. They're overrated. T-shirt shops, a mime or two, and seafood sold in cups on the street. If you want oysters/clams etc, go to Anchor Stea Bar in teh Castro.Pier 39 is worth visiting if the seals/sealions are there on their floating docks. Unpredictable if they will be there or not. There's an aquarium (I haven't been). The DeYoung museum in GG Park, if you're into art (also the Science Academy across the road from the museum - that's really worth visiting). If you're into plants, an arboretum and separate conservatory - also in GG Park. Marina Green and GG Park are great places for running. Walk across the Golden Gate bridge. One can rent bicycles lots of places, and ride across the bridge. If you drive across the bridge, NB, you have to make arrangements to pay the toll coming back - there are no toll takers
and EZPass doesn't work here. Get something to eat at the Cliff House. Greens (famous vegetarian restaurant) is overrated, but has nice views - on the water. Chez Panisse in Berkeley is way overrated and overpriced. Hot new restaurants are along Valencia Street. Best Chinese restaurants along Geary or Clement - out in the avenues. Several dim sum places downtown. Inquire on Trip Advisor if you want to go to Muir Woods (redwoods) - parking is difficult. Equally magnificent redwoods in Henry Cowell Redwoods State Park - near Santa Cruz - can be combined with a trip to Santa Cruz, Monterey (great aquarium), Carmel by the Sea, and Big Sur hiking.
If it's warm (October is sometimes the hotest time of year) you can go to the beach - Huge Ocean Beach is for lying on the sand only ( too dangerous for swimming - tourists are always getting swept out to sea while wading, and drown). Lands End Beach, China Beach (lifeguard) and Baker Beach are swimable. Baker Beach has some nude gay men. Lands End used to have nude sunbathing, but since they made it "accessible," park rangers with too much time on their hands occasionally cite people for being suitless. If it s really warm, it may be worth a drive south to San Gregorio (north of the official San Gregorio park beach) a popular gay nude sunbathing beach (think Fire Island dunes without trees). Or north to Red Rock Beach (just south of Stinson Beach) - has two very small parking lots - have to go very early on a weekend. I remember one October 30 when it was warm enough there to stay in the water for a half hour. When you're coming downhill on Highway 1 toward Stinson Beach, and you see a parking lot on the side of the road, you are there.
Having lived here for 20+ years, I don't do much here that is touristy, but I know a lot. PM me if you have any questions.