Just a few quick thoughts:
- Depending on time of day, traffic on the Bay Bridge is no joke.
- If you're open to taking public transportation, you can take BART from OAK to Embarcadero station for about $11/person. The Hyatt is pretty much right outside Embarcadero station. https://www.bart.gov
- Note that Uber rates in San Francisco are the highest in the country, but there's no shortage of Ubers.
- I wouldn't say the Hyatt near the Embarcadero is closer than the Hyatt at Fisherman's Wharf to the ferries to Alcatraz. The Alcatraz ferries depart from Pier 33, about halfway between the two Hyatts on the Embarcadero. The Hyatt at the Wharf may actually be closer. You can take the Muni F-line street car from either Hyatt (heading in opposite directions) to Pier 33. Adult fare is $2.75. https://www.sfmta.com/muni and http://www.nextmuni.com/
- The Hyatt at the Embarcadero is a short walk away from the Ferry Building, which has a lot of local artisanal craft and upscale dining options. https://www.ferrybuildingmarketplace.com/merchants/
- There's a farmers market at the Ferry Building on Tuesdays and Thursdays, but the biggest (and famous) one is on Saturdays. If you're foodies, it's a must visit. https://www.ferrybuildingmarketplace.com/farmers-market/
- The Hyatt is also very convenient to Chinatown. I'm all for the authentic experience and you can still find some of that in Chinatown, but a lot of the Chinese have moved their businesses and restaurants to the Richmond and Sunset neighborhoods and Daly City. However, you should make it a point to check out Mister Jiu's, which took over the historic Four Seas banquet restaurant space and has been winning rave reviews for elevating Chinese cuisine with Californian influences. http://misterjius.com Some of my favorite places for dim sum in Chinatown/Financial District are Great Eastern, City View, and Yank Sing. If you can make it out to the Richmond, there's great dim sum at Dragon Beaux, Hong Kong Lounge I and II. There's also the Golden Gate Fortune Cookie Factory in Chinatown. https://freetoursbyfoot.com/visit-san-franciscos-fortune-cookie-factory/
- Chinatown is very close to North Beach, which is a historically Italian-American neighborhood. You might want to check out the historic City Lights Bookstore right at the edge of Chinatown and North Beach. http://www.citylights.com For food, Tony’s Pizza Napoletana has great award-winning pizza! http://tonyspizzanapoletana.com We take our brunch seriously in the city and every neighborhood has one or several popular brunch spots. In North Beach, there's Mama's and I swear their Monte Cristo is better than the one at Cafe Orleans and Blue Bayou. http://www.mamas-sf.com Get there early, or be prepared to line up for an hour or more.
- From your hotel to AT&T Park is very easy. Go to Embarcadero station to catch the Muni light rail lines N or T heading south towards the ballpark. (Embarcadero station serves both BART (lower level) and Muni's light rail (upper level).)
- If you're planning to visit the Walt Disney Family Museum, you can probably see everything in a few hours.
- Since you're staying at the Hyatt near the Embarcadero, there's a free PresidiGo shuttle that stops right in front of the Hyatt that'll take you all the way to the Presidio Transit Center. (It also stops at the Letterman Digital Arts Building on the way, where there's the Yoda statue fountain.) The Presidio Transit Center is right next to the Visitor Center and less than a five minute walk to the Walt Disney Family Museum. When you're done, you can take the PresidiGo shuttle back to your hotel. https://www.presidio.gov/transportation/presidigo
- As @afan mentioned, SF Pride is on June 23 and 24 this year, but the week before will see a lot of people coming into the city for the festivities. Market Street and the Civic Center will be impossible to get around that weekend.
I've tried to avoid the usual tourist spots like Union Square, Cable Cars, Coit Tower, Lombard Street, Ghirardelli Square, Pier 39, but those are worth visiting if they're already in your plans or you have the time.
ETA: If you want to see Union Square, Ghirardelli Square, ride the Cable Car, then Fisherman's Wharf, you can do all of them in one trip that'll take maybe half a day.
From the Hyatt Regency, you'll want to go up Market Street. You can walk it (but this mostly takes you through the Financial District), or hop on the F-line streetcar for a historic experience (or ride any of the other Muni buses or light rail underground up Market). Stop at Powell Street or Powell Street station. Up the hill is Union Square and across the street is the Westfield Emporium mall. In front of the Gap is the cable car turnaround. You'll probably have to wait in line, but the cable car ($7/person) will take you up over Nob Hill and Russian Hill and you'll end up right outside Ghirardelli Square. I haven't been to Ghirardelli Square in years, but there's a Ghirardelli shop there for chocolate and ice cream that'll make a fun stop since there's also a Ghirardelli in Disney California Adventure. From Ghirardelli Square, it's an easy walk down the hill to Fisherman's Wharf where there's In-n-Out, Boudin, seafood stands and classic restaurants. Catch the F-line along the Embarcadero back to the Hyatt Regency.
Outside of the city, you can walk or (rent a bike and) bike across the Golden Gate Bridge, then return by ferry from Sausalito.
https://freetoursbyfoot.com/bike-across-golden-gate-bridge-ferry-back/ Or visit Muir Woods.
https://www.nps.gov/muwo/planyourvisit/index.htm
Ok. All that took a lot longer to type out than it did to think up. So I'll leave it here. If you have any other questions or want more tips, just let me know.