score:11
I used to live near Regent's Park and used to pass through on foot after closing times. I also took evening courses at LSE which let out after closing times. Starting from the Parish Church on Marylebone Road, you can take York Street and turn right after you cross the Outer Circle. This will take you to a wide grassy field abuting a children's playground. It's an area of the park called "Marylebone Green" in which you can star gaze. In this area you are also likely to see walkers returning from Marylebone to Primrose Hill. Depending upon the season, you may also see street urchins near the tennis courts collecting stray tennis balls. They may be undesirable company.
There are other areas of the park which also can be reached from York Road/York Gate. Hyde Park is less restricted than Regent's Park and you would be able to star gaze in the grassy fields immediately south of Marble Arch.
Take care. I'm also a member of a neighbourhood association in Marylebone which has called for an alert on people molesting the swans at night. If you wander too close to the ponds, you might find a neighbourhood vigilante calling you in. Locals take those sorts of things with formidable gravitas. Also avoid the ducks who might be feeding in the grassy areas.
The comment by gsnedders (to whom thanks) correctly points out that portions of the park are gated and if you get caught entering a gated area you'll get a police caution. Accordingly, stay away from the Inner Circle in Regent's Park and other gated areas like in Hyde Park.
Generally, the overall public mood is 'live and let live' and that patrolling the park for out-of-hours violations is rather far down the list of police priorities. As long as you are not in a gated area and you have a reasonable premise, you'll be fine.