There really is no great way I know of to get through Richmond on your proposed ride. I think the best option is the one you already spotted - via Richmond Parkway and Castro Street. Yeah, they can be trafficky, but they have bike lanes and avoid sketchy neighborhoods, of which Richmond has plenty.
My thought is to turn right off the Al Zampa-Carquinez Bridge and go past the Dead Fish. This is San Pablo Avenue. Stay on it until the Richmond Parkway, then turn right. Be careful in Rodeo - you have to bear right at an intersection at the far end of downtown (from your perspective) to stay on San Pablo Ave. If you get to I-80, you've gone too far.
As for a coffee shop, I do not have a specific recommendation and nothing with a Bay view. However, Pt Richmond has a number of coffee shops and other refreshment opportunities and it's a pleasant area. To get there, at the end of Castro St (you have literally just gone under the I-580 freeway). turn left onto Tewksbury St. (The entrance to the SR Bridge bike path will be on your right at this intersection.) You would turn right here to get on the San Rafael Bridge trail. Ride a short distance and turn right onto either Washington (the "A" option) or Railroad (the "A-" option), and start looking for something that looks good to you. Retrace your steps west along Tewksbury back to the SR Bridge path entrance, and continue on your merry way.
A word of advice for the SR side of the bridge. The path will deposit you onto the northside frontage road for I-580. If you are headed straight into downtown San Rafael, no worries - just go straight. If you want to use the overpass (legal, with a separate bike path, like the bridge) and go through Larkspur Landing on Sir Francis Drake Blvd., keep you eyes peeled for the entrance to the path on your left. If you are looking for it, it's easy to spot. If you aren't actively looking for it, it's not hard to miss.
Have a great ride.
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