Probably option one, then, it would have stayed where it was, stationary.
Although 'stationary' is relative. And technically it's in an upward-accelerating frame of reference w.r.t. local spacetime if it is 'stationary' to the mass of the Earth, plus some subtle offset due to Coriolis effects. I think we must accept the concept that upon being 'irrevocably protected', the field 'anchors' to at least the first derivative of motion of the local frame, instantaneous to activation. Which means that if you had destroyed (or removed) the whole planet Earth, without shutting off the protective field, would it have considered to rotate in space, every 24 hours, 'orbiting' around Earth's projected barycentre, in turn epicyclicly travelling around the Sun. Or in turn following the path of the Sun through the local stellar neighbourhood, turning around galactic centre... If you could be selective about which frames of reference a device such as this persistently follows, with enough control it could be an excellent way of 'travelling by not travelling'. Assuming you could calculate an appropriate combination of relative motions to observe.
(This is just one issue one needs to ask of Doc Brown, regarding the operation of his Delorean. Travel across time seems locked to local geography, but apart from all the above motions-upon-motions, there's also the likelihood of tectonic plate movements that would introduce some slight repositioning, even if it's just half of the reported "same as the rate of growth of fingernails"/whatever mid-Atlantic ridge separation rate, over the +/-30 years or so, for the North American plate, relative to... what? Oh, wait, Hollywood is the centre of the universe, so I suppose it depends on which side of various faults Hill Valley, CA, lies, w.r.t. the site of the Hollywood(Land) Sign hill itself, naturally.)
((...well, this thread is for nitpicks. Although I didn't actually have that in mind when I first started down this particular train of thought.))