You're gonna need a car big enough for 8 people! Or two. Either will be hard to park in SF. On the other hand, 8 fares for transit, train or airline won't be cheap either. That vs the value of 8 peoples' time.
Beware, USA credit card readers aren't all ready for chip cards. Many still need magnetic stripe, including all gasoline stations. Target shops are all chip, and they sell Mastercard gift cards which have stripes.
San Jose to San Francisco
A "short drive" that soon turns into 2+ hours with commute traffic. You'll spend more time in SF trying to park than actually seeing anything. (2 spots near each other? forget it unless you use expensive garages.)
Take CalTrain. Trains every 30-60 minutes, some are express.
CalTrain requires Proof-of-Payment. You must buy and validate a ticket at the station before you board. A fare inspector might appear and check it.
You can fool around with driving to BART if you really want to, but the closest BART gets to San Jose is Fremont, the drive there is long and very congested, and BART parking is nigh impossible. BART uses stored-value cards exactly like Washington DC Metro. It also supports Clipper.
Inside San Francisco
While in the City proper, use taxi/Uber/Lyft, or the Muni public transit system, which is excellent.** Many drug and liquor stores sell Muni Maps. You pay for Muni one of several ways:
- $2.50 cash fare. You >>MUST<< take a transfer (proof of payment again), good for unlimited additional rides on Muni for 90 minutes (longer if you get it from a human driver). Human drivers can also take a $5 bill and give you 2 transfers. Other than that, human drivers need exact change. Transit works can't give change and local shops don't like to. In the underground, you buy tickets from the machines.
- Clipper. This is a cash-storage smartcard that works on all the systems I'm mentioning.
- Muni Passport. This is for tourists, it's a 1, 3 or 7 day "all-Muni pass" which includes the Historic Cable Cars. You buy it downtown near the Embarcadero or Powell St cable car terminals.
("the City" capitalization was a style of a beloved newspaper columnist named Herb Caen. Many will appreciate the reference.)
San Francisco to Berkeley/Oakland
Just for reference -- BART does that. Trains every 7-20 minutes, also SFO and OAK airports.
San Jose to Berkeley/Oakland
Just for reference -- Amtrak Capitol Corridor does that. 15 trains/day (really), hourly-ish. Also stops at Coliseum for OAK airport. No Clipper.
Yosemite
Drive. Period. There's no other transit.
Prepare for big Sierra snow - heavy, deep and fluffy, unlike the dreary, icy snow of the American east. California does not use road salt because it's a different kind of snow.
So many California drivers have zero experience driving in snow at all, that CalTrans is surprisingly draconian about things like chains. Yes, chains on cars. Welcome to California.
San Jose to Las Vegas
Driving: Seems like a bad idea unless you do a San Jose - Las Vegas - Los Angeles triangle. This is the worst side of the triangle, don't do it twice if you can avoid it. I hate it, and I don't even do the worst part, Pacheco Pass.
It's a circuitous route and a 9 hour drive, barring traffic or snow. There are 3 gigantic "freeway gaps" (Pacheco Pass US-101 to I-5, I-5 to CA-99, and Boron/Kramer Jct) and you'll spend half your time behind a slow truck thinking "I thought freeways were a thing here". There will be risk of snow/ice in Pacheco and Tehachapi passes, and in Nevada... but not the crazy Sierra stuff.
Flying: SJC is a "737 airport". It's made for regional hops, and the flights to LAS are thick and cheap, since it's a huge tourist destination for the natives. Southwest has 9 direct flights, Delta has 3. (warning: Southwest is a great airline but not on the booking sites, deal direct.)
The Las Vegas Strip area is almost walkable, and transit, cabs and Uber etc. are readily available. There's even a monorail (plus 2 more monorails within casinos), most free for any comer.) Casinos do not like under-21 people in the casino proper, but will sometimes turn a blind eye to passersby who are not gambling. The shopping is gigantic.
Las Vegas to Los Angeles
Just for reference: Flying: plenty of flights. Driving: easy by comparison, 4 hours all freeway. Possible snow in Nevada and Cajon Pass.
San Jose to Los Angeles
Many decent options, no great ones.
Flying: again SJC is the perfect airport, and flights are thick and cheap to LAX, Burbank, John Wayne, Ontario or the utterly charming Long Beach. (Again, as these are largely commuter hops, the big carriers Southwest, Alaska or Jetblue are not on the booking sites). But then you won't have a car, and that's a problem because L.A. is enormous.
The Coast Starlight train is magnificent, a tourist adventure all to itself. But it's rather slow. (and often late, since long trains accumulate delays, and southbound came from Seattle, so if you go one-way, prefer northbound for less delays.) For what it's worth, Amtrak comes into the main transit hub, Union Station. But it's hard for L.A. to have good public transit over such a vast area.
Driving: Again, getting to I-5 is ugly, but then it's all freeway. Risk of weather in Pacheco Pass and the Grapevine. You can also reach I-5 via Altamont Pass instead of Pacheco for a 100% freeway route (I-680 to I-580 to reach I-5) but it is vulnerable to crushing traffic jams.
If you find yourself driving I-5, a great spot to take a break is Harris Ranch at Coalinga. It's about halfway in the SJ-LA run.
You can bypass I-5 ugliness by taking US-101 the whole way, which is all 4-lane, prettier, and maybe 1 hour slower. It may matter where in L.A. you are trying to go. Ask your maps app.
For a really beautiful drive, add 2 more hours and take CA-1 (the Pacific Coast Highway). Route to Monterey then stay on Highway 1 through San Simeon, Lompoc and Malibu.
By the way, this is about those road numbers.
** I mention Muni being excellent, to counteract two stereotypes: first from non-Californians that California is all cars and transit is terrible (not in SF!). And second, from City residents who say Muni is awful; yes it is flawed and underfunded, but it is a world-class transit system that is flawed and underfunded. And it has cable cars!