Travel Note
Alameda is very cute. East End Alameda puts you closer to R&J's home, but the whole island is awesome. The list also includes some places in the Oakland hills, which is closer to the wedding venue. If you don't rent a car, choose Oakland and search for lodging near BART stations, like a swanky high rise in downtown Oakland, a cute place in Rockridge neighborhood, or a house in Fruitvale neighborhood. It's easy to Lyft or Uber to/from the wedding venue.
Rental Car
We have found Costco Travel to have the best car rental prices. If you're a member, definitely try them. They have free cancelations and prices do change, so you can keep checking and book at new lower rates as they come up.
Train
Fairly easy to navigate if you have any experience with public transit. Download the CLIPPER app on your phone to pay the fare. Tap to enter and tap to exit stations. View the BART website linked below to get more info on Clipper app, and to view schedules, fares, etc.
Flight
Oakland Airport is closest and is a lovely smaller airport than SFO. Lots of Southwest flights. Easily connect to BART train or rental car hub.
Flight
Depending on the city you're traveling from, SFO is likely to have the most options for direct flights. It's a long and slightly pricey Uber ride to Oakland, but BART is inexpensive and fairly easy if you can manage public transit without breaking into a stress-induced cold sweet. :) Easy to get car rentals from here too (ride the free airport tram right to the car rental area).
Flight
San Jose airport is a little further from Oakland than SFO is, but they do have some good direct flight options. S0 depending on your departure city, this could be a way better option for you than SFO. I'm looking at you, Nashville SW crew :) Definitely get a car rental if you're flying to SJC. Put on a podcast and don't let the 880 traffic get to you... you're in California now, so relax!