Here's the configuration with bike lanes on each side. The schematic shows car parking on one side of the street. In other sections of the road there would be insufficient room for any parking, and the buffers would be wider:
Here's a schematic of the configuration with the lanes on the same side, in the case where car parking is on the same side as the lanes (the parking could also be on the opposite curb):
The San Francisco Bike Coalition has promoted the one-sided configuration. They publish artists renderings of cheerful cyclists pedaling in the sun in green-painted lanes. It's part of their "Connecting the City" campaign.
However, there's two serious issues with the one-sided configuration. One is that at some point the lanes end. At each end, one direction must transition between the left and right of the road. This requires first crossing on-coming vehicular traffic, then merging with cars moving in the same direction. Usually when you merge with traffic, you look over your shoulder to make sure it's clear, but since you're facing on-coming car traffic at this point looking backward must be done with exceptional care. Even with a mirror, which reduces the head movement required to look back, your attention is removed from the on-coming lane. The same problem occurs for cyclists making left-hand turns: doing so requires crossing first the on-coming bike lane, then an on-coming vehicle lane, and finally the lane of car traffic moving in the same direction. There is enormous opportunity for failure here.
Another problem with the one-sided configuration is pedestrians, who in the park are often distracted tourists or children, must now check for bikes from the left, then bikes from the right, then cars from the left, then cars from the right in order to cross the street. With the lanes on each side of the road, cars and bikes are from the left, then cars and bikes are from the right. This latter case is the one which we've been trained most of our lives to handle. I don't have statistics to back this up, but it seems an inattentive pedestrian is at fare greater risk, and presents a far greater risk, in the one-sided configuration.
The two-sided configuration isn't great, either. With the bike lane between the parked cars and the curb, drivers moving between their vehicles and the side of the street need to watch for bikes. I'm not too worried about this: the 5-foot buffers should help. But on the 2-sided scenario cars may be parked on the side opposite the bike lanes.
So what's the solution? Of the two, I far prefer the two-sided set-up. And the much-neglected California Highway Design Manual chapter 1000 (PDF) agrees:
Class II bike lanes shall be one-way facilities. Two-way bike lanes (or bike paths that are contiguous to the roadway) are not permitted, as such facilities have proved unsatisfactory and promote riding against the flow of motor vehicle traffic.
Sure, the two-sided plan results in the loss of additional car parking, but car parking is not and should not be the priority here. The roads are primarily for transportation, and space is too precious in the city.
This may be controversial, but the City Charter has since 1978 been quite clear on the matter: San Francisco has a transit-first policy. But "transit first" doesn't simply promote mass-transit: it prioritizes all nonvehicular transportation. It's really worthwhile reading the whole thing, but here's an extract:
8A.115.3: Decisions regarding the use of limited public street and sidewalk space shall encourage the use of public rights of way by pedestrians, bicyclists, and public transit, and shall strive to reduce traffic and improve public health and safety.
This cuts straight to the core of the JFK issue. There's two reasons to allow cars in the park. One is to allow drivers to access the park itself. The other is to provide transportation from one side of the park to the other. But the presence of the cars here actively impedes park users who aren't in cars. Cyclists and pedestrians are not only endangered by all of the vehicles, but the noise from all the auto traffic spoils the tranquility which should be provided by the precious resource which is Golden Gate Park. If we want to encourage access by pedestrians, bicyclists, and public transit, if we are striving to reduce traffic in the park and improve public health and safety, the obvious approach is to extend the Sunday daylight restriction against motor vehicle access to JFK to 24-7. There's other roads into the Park, like Kezar and 19th Ave. JFK serves no critical purpose other than to facilitate and promote automobile use.
New York City is way ahead of San Francisco in many ways, and this is one of them: cars have been restricted from Central Park (except for 4 hours per day M-F) for many years. San Francisco need only follow its example.